Heat and Thermodynamics
486 Questions
2020
JEE Mains
Numerical
JEE Main 2020 (Online) 3rd September Evening Slot
If minimum possible work is done by a refrigerator in converting 100 grams of water at 0oC to ice,
how much heat (in calories) is released to the surroundings at temperature 27oC (Latent heat of
ice = 80 Cal/gram) to the nearest integer ?
Correct Answer: 8791
Explanation:
Q1 = mL = 8000cal
Q2 = W + Q1
Coefficient of performance (C.O.P)
$ = {{{Q_1}} \over W} = {{{Q_1}} \over {{Q_2} - {Q_1}}} = {{{T_1}} \over {{T_2} - {T_1}}}$
${{{Q_1}} \over W} = {{273} \over {300 - 273}}$
${{{Q_1}} \over W} = {{273} \over {27}}$
$W = {{27} \over {273}}{Q_1}$
$W = {{27} \over {273}}mL$
$W = {{27} \over {273}} \times 80 \times 100$
${Q_2} = {{27} \over {273}} \times 80 \times 100 + 80 \times 100$
$ = 8791.2$ cal
Q2 = W + Q1
Coefficient of performance (C.O.P)
$ = {{{Q_1}} \over W} = {{{Q_1}} \over {{Q_2} - {Q_1}}} = {{{T_1}} \over {{T_2} - {T_1}}}$
${{{Q_1}} \over W} = {{273} \over {300 - 273}}$
${{{Q_1}} \over W} = {{273} \over {27}}$
$W = {{27} \over {273}}{Q_1}$
$W = {{27} \over {273}}mL$
$W = {{27} \over {273}} \times 80 \times 100$
${Q_2} = {{27} \over {273}} \times 80 \times 100 + 80 \times 100$
$ = 8791.2$ cal
2020
JEE Mains
Numerical
JEE Main 2020 (Online) 3rd September Morning Slot
A bakelite beaker has volume capacity of 500 cc at 30oC. When it is partially filled with Vm
volume
(at 30oC) of mercury, it is found that the unfilled volume of the beaker remains constant as
temperature is varied. If $\gamma $(beaker) = 6 × 10–6 oC–1 and $\gamma $(mercury) = 1.5 × 10–4 oC–1, where $\gamma $ is the
coefficient of volume expansion, then Vm
(in cc) is close to ____.
Correct Answer: 20
Explanation:
$\Delta $V = V$\gamma $$\Delta $T
$ \therefore $ V1$\gamma $1 = V2$\gamma $2
$ \Rightarrow $ 500 $ \times $ 6 $ \times $ 10-6 = Vm $ \times $ 1.5 $ \times $ 10-4
$ \Rightarrow $ Vm = ${{500 \times 6 \times {{10}^{ - 6}}} \over {1.5 \times {{10}^{ - 4}}}}$
$ \Rightarrow $ Vm = 20 cc
$ \therefore $ V1$\gamma $1 = V2$\gamma $2
$ \Rightarrow $ 500 $ \times $ 6 $ \times $ 10-6 = Vm $ \times $ 1.5 $ \times $ 10-4
$ \Rightarrow $ Vm = ${{500 \times 6 \times {{10}^{ - 6}}} \over {1.5 \times {{10}^{ - 4}}}}$
$ \Rightarrow $ Vm = 20 cc
2020
JEE Mains
Numerical
JEE Main 2020 (Online) 2nd September Morning Slot
An engine takes in 5 moles of air at 20oC and
1 atm, and compresses it adiabatically to
1/10th of the original volume. Assuming air to
be a diatomic ideal gas made up of rigid
molecules, the change in its internal energy
during this process comes out to be X kJ. The
value of X to the nearest integer is________.
Correct Answer: 46
Explanation:
For diatomic ideal gas :
f = 5
$\gamma $ = ${7 \over 5}$
Ti = T = 273 + 20 = 293 K
Vi = V
Vf = ${V \over {10}}$
For adiabatic process TV$\gamma $ - 1 = constant
${T_1}V_1^{\gamma - 1} = {T_2}V_2^{\gamma - 1}$
$ \Rightarrow $ $\left( {293} \right){V^{{7 \over 5} - 1}} = {T_2}{\left( {{V \over {10}}} \right)^{{7 \over 5} - 1}}$
$ \Rightarrow $ ${T_2} = 293 \times {\left( {10} \right)^{{2 \over 5}}}$
$\Delta $U = ${{nfR\left( {{T_2} - {T_1}} \right)} \over 2}$
= ${{5 \times 5 \times {{25} \over 3} \times \left( {{{293.10}^{{2 \over 5}}} - 293} \right)} \over 2}$
= ${{625 \times 293 \times \left( {{{10}^{{2 \over 5}}} - 1} \right)} \over 6}$
= 46.14 $ \times $ 103 J
$ \simeq $ 46 kJ
f = 5
$\gamma $ = ${7 \over 5}$
Ti = T = 273 + 20 = 293 K
Vi = V
Vf = ${V \over {10}}$
For adiabatic process TV$\gamma $ - 1 = constant
${T_1}V_1^{\gamma - 1} = {T_2}V_2^{\gamma - 1}$
$ \Rightarrow $ $\left( {293} \right){V^{{7 \over 5} - 1}} = {T_2}{\left( {{V \over {10}}} \right)^{{7 \over 5} - 1}}$
$ \Rightarrow $ ${T_2} = 293 \times {\left( {10} \right)^{{2 \over 5}}}$
$\Delta $U = ${{nfR\left( {{T_2} - {T_1}} \right)} \over 2}$
= ${{5 \times 5 \times {{25} \over 3} \times \left( {{{293.10}^{{2 \over 5}}} - 293} \right)} \over 2}$
= ${{625 \times 293 \times \left( {{{10}^{{2 \over 5}}} - 1} \right)} \over 6}$
= 46.14 $ \times $ 103 J
$ \simeq $ 46 kJ
2020
JEE Mains
Numerical
JEE Main 2020 (Online) 9th January Evening Slot
Starting at temperature 300 K, one mole of an
ideal diatomic gas ($\gamma $ = 1.4) is first compressed
adiabatically from volume V1 to V2 = ${{{V_1}} \over {16}}$. It is
then allowed to expand isobarically to volume 2V2. If all the processes are the quasi-static then
the final temperature of the gas (in oK) is (to the nearest integer) _____.
ideal diatomic gas ($\gamma $ = 1.4) is first compressed
adiabatically from volume V1 to V2 = ${{{V_1}} \over {16}}$. It is
then allowed to expand isobarically to volume 2V2. If all the processes are the quasi-static then
the final temperature of the gas (in oK) is (to the nearest integer) _____.
Correct Answer: 1818TO1819
Explanation:
T1V1$\gamma $–1 = T2V2
$\gamma $–1
$300 \times {V^{{7 \over 5} - 1}} = {T_2}{\left( {{V \over {16}}} \right)^{{7 \over 5} - 1}}$
$ \Rightarrow $ T2 = 300 × (16)0.4
Isobaric process
V = ${{nRT} \over P}$
V2 = kT2... (1)
2V 2 = KTf... (2)
Tf = 2T2 = 300 × 2 × (16)0.4 = 1818 K
$300 \times {V^{{7 \over 5} - 1}} = {T_2}{\left( {{V \over {16}}} \right)^{{7 \over 5} - 1}}$
$ \Rightarrow $ T2 = 300 × (16)0.4
Isobaric process
V = ${{nRT} \over P}$
V2 = kT2... (1)
2V 2 = KTf... (2)
Tf = 2T2 = 300 × 2 × (16)0.4 = 1818 K
2020
JEE Mains
Numerical
JEE Main 2020 (Online) 8th January Evening Slot
Three containers C1, C2 and C3 have water at
different temperatures. The table below shows
the final temperature T when different amounts
of water (given in litres) are taken from each
containers and mixed (assume no loss of heat
during the process)
The value of $\theta $ (in °C to the nearest integer) is ..........
The value of $\theta $ (in °C to the nearest integer) is ..........
Correct Answer: 50
Explanation:
Let containers C1, C2, C3 contain water at T1, T2 and T3 temperatures respectively.
Applying law of calorimetry
1(T1 – 60) + 2(T2 – 60) = 0
$ \Rightarrow $ T1 + 2T2 = 180 ....(1)
1(T2 – 30) + 2(T3 – 30) = 0
$ \Rightarrow $ T2 + 2T3 = 90 ......(2)
2(T1 – 60) + 1(T3 – 60) = 0
$ \Rightarrow $ 2T1 + T3 = 180 .....(3)
from (1), (2), (3)
T1 = 80o C
T2 = 50o C
T3 = 20o C
1 × (T1 – $\theta $) + 1 ×(T2 – $\theta $) + 1(T3 – $\theta $) = 0
$ \Rightarrow $ T1 + T2 + T3 = 3$\theta $
$ \Rightarrow $ $\theta $ = ${{80 + 50 + 20} \over 3}$ = 50oC
Applying law of calorimetry
1(T1 – 60) + 2(T2 – 60) = 0
$ \Rightarrow $ T1 + 2T2 = 180 ....(1)
1(T2 – 30) + 2(T3 – 30) = 0
$ \Rightarrow $ T2 + 2T3 = 90 ......(2)
2(T1 – 60) + 1(T3 – 60) = 0
$ \Rightarrow $ 2T1 + T3 = 180 .....(3)
from (1), (2), (3)
T1 = 80o C
T2 = 50o C
T3 = 20o C
1 × (T1 – $\theta $) + 1 ×(T2 – $\theta $) + 1(T3 – $\theta $) = 0
$ \Rightarrow $ T1 + T2 + T3 = 3$\theta $
$ \Rightarrow $ $\theta $ = ${{80 + 50 + 20} \over 3}$ = 50oC
2020
JEE Mains
Numerical
JEE Main 2020 (Online) 7th January Evening Slot
M grams of steam at 100oC is mixed with 200 g of ice at its melting point in a thermally insulated
container. If it produced liquid water at 40oC [heat of vaporization of water is 540 cal/g and heat
of fusion of ice is 80 cal/g] the value of M is ____
Correct Answer: 40
Explanation:
M × 540 + M + 60 = 200 × 80 + 200 × 1× (40– 0)
$ \Rightarrow $ 600 M = 24000
$ \Rightarrow $ M = 40
$ \Rightarrow $ 600 M = 24000
$ \Rightarrow $ M = 40
2020
JEE Mains
Numerical
JEE Main 2020 (Online) 7th January Morning Slot
A non-isotropic solid metal cube has coefficients of linear expansion as :
5 $ \times $ 10-5/oC along the x-axis and 5 $ \times $ 10-6/oC along the y and the z-axis. If the coefficient of volume expansion of the solid is C $ \times $ 10-6/oC then the value of C is
5 $ \times $ 10-5/oC along the x-axis and 5 $ \times $ 10-6/oC along the y and the z-axis. If the coefficient of volume expansion of the solid is C $ \times $ 10-6/oC then the value of C is
Correct Answer: 60
Explanation:
$\gamma $ = $\alpha $x + $\alpha $y + $\alpha $z
$ \Rightarrow $ C $ \times $ 10–6 = 5 × 10–5 + 5 × 10–6 + 5 × 10–6
$ \Rightarrow $ C $ \times $ 10–6 = 50 × 10–6 + 10 × 10–6
$ \Rightarrow $ C = 60
$ \Rightarrow $ C $ \times $ 10–6 = 5 × 10–5 + 5 × 10–6 + 5 × 10–6
$ \Rightarrow $ C $ \times $ 10–6 = 50 × 10–6 + 10 × 10–6
$ \Rightarrow $ C = 60
2020
JEE Mains
Numerical
JEE Main 2020 (Online) 7th January Morning Slot
A Carnot engine operates between two reservoirs of temperatures 900 K and 300 K. The engine
performs 1200 J of work per cycle. The heat energy (in J) delivered by the engine to the low
temperature reservoir, in a cycle, is _______.
Correct Answer: 600
Explanation:
So ${{Q + 1200} \over Q} = {{900} \over {300}}$
$ \Rightarrow $ Q + 1200 = 3Q
$ \Rightarrow $ Q = 600 J
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 12th April Evening Slot
A diatomic gas with rigid molecules does 10 J of work when expanded at constant pressure. What would be
the heat energy absorbed by the gas, in this process ?
A.
35 J
B.
30 J
C.
25 J
D.
40 J
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 12th April Evening Slot
One kg of water, at 20oC, heated in an electric kettle whose heating element has a mean (temperature
averaged) resistance of 20 $\Omega $. The rms voltage in the mains is 200 V. Ignoring heat loss from the kettle, time
taken for water to evaporate fully, is close to :
[Specific heat of water = 4200 J/(kg oC), Latent heat of water = 2260 kJ/kg]
A.
10 minutes
B.
22 minutes
C.
3 minutes
D.
16 minutes
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 12th April Evening Slot
A Carnot engine has an efficiency of ${1 \over 6}$. When the temperature of the sink is reduced by 62ºC, its efficiency
is doubled. The temperatures of the source and the sink are, respectively
A.
99oC, 37oC
B.
124oC, 62oC
C.
37oC, 99oC
D.
62oC, 124oC
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 12th April Morning Slot
At 40o C, a brass wire of 1 mm radius is hung from the ceiling. A small mass, M is hung from the free end of
the wire. When the wire is cooled down from 40oC to 20oC it regains its original length of 0.2 m. The value
of M is close to :
(Coefficient of linear expansion and Young’s modulus of brass are 10–5
/oC and 1011 N/m
2
, respectively; g=
10 ms–2
)
A.
1.5 kg
B.
0.5 kg
C.
9 kg
D.
0.9 kg
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 12th April Morning Slot
Two moles of helium gas is mixed with three moles of hydrogen molecules (taken to be rigid). What is the
molar specific heat of mixture at constant volume ? (R = 8.3 J/mol K)
A.
21.6 J/mol K
B.
17.4 J/mol K
C.
15.7 J/mol K
D.
19.7 J/mol K
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 12th April Morning Slot
When M1 gram of ice at –10oC (specific heat = 0.5 cal g–1
oC–1
) is added to M2 gram of water at 50C, finally
no ice is left and the water is at 0°C. The value of latent heat of ice, in cal g–1
is :
A.
${{50{M_2}} \over {{M_1}}} - 5$
B.
${{50{M_2}} \over {{M_1}}}$
C.
${{5{M_2}} \over {{M_1}}} - 5$
D.
${{5{M_1}} \over {{M_2}}} - 50$
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 12th April Morning Slot
A sample of an ideal gas is taken through the cyclic process abca as shown in the figure. The change in the
internal energy of the gas along the path ca is –180 J. The gas absorbs 250 J of heat along the path ab and 60
J along the path bc. The work done by the gas along the path abc is:
A.
120 J
B.
130 J
C.
100 J
D.
140 J
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 10th April Evening Slot
One mole of ideal gas passes through a process where pressure and volume obey the relation
$P = {P_0}\left[ {1 - {1 \over 2}{{\left( {{{{V_0}} \over V}} \right)}^2}} \right]$.
Here P0 and V0 are constants. Calculate the change in the temperature of the gas if its
volume changes form V0 to 2V0
A.
${3 \over 4}{{{P_0}{V_0}} \over R}$
B.
${1 \over 2}{{{P_0}{V_0}} \over R}$
C.
${5 \over 4}{{{P_0}{V_0}} \over R}$
D.
${1 \over 4}{{{P_0}{V_0}} \over R}$
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 10th April Evening Slot
When heat Q is supplied to a diatomic gas of rigid molecules, at constant volume its temperature increases by
$\Delta $T. the heat required to produce the same change in temperature, at a constant pressure is :
A.
${7 \over 5}Q$
B.
${3 \over 2}Q$
C.
${2 \over 3}Q$
D.
${5 \over 3}Q$
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 10th April Morning Slot
A cylinder with fixed capacity of 67.2 lit
contains helium gas at STP. The amount of heat
needed to raise the temperature of the gas by
20°C is : [Given that R = 8.31 J mol–1 K–1]
A.
374 J
B.
700 J
C.
748 J
D.
350 J
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 10th April Morning Slot
n moles of an ideal gas with constant volume
heat capcity CV undergo an isobaric expansion
by certain volume. The ratio of the work done
in the process, to the heat supplied is :
A.
${{nR} \over {{C_V} - nR}}$
B.
${{4nR} \over {{C_V} - nR}}$
C.
${{4nR} \over {{C_V} + nR}}$
D.
${{nR} \over {{C_V} + nR}}$
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 10th April Morning Slot
A 25 × 10–3 m3 volume cylinder is filled with
1 mol of O2 gas at room temperature (300K).
The molecular diameter of O2, and its root
mean square speed, are found to be 0.3 nm, and
200 m/s, respectively. What is the average
collision rate (per second) for an O2 molecule ?
A.
~1013
B.
~1012
C.
~1011
D.
~1010
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 9th April Evening Slot
The specific heats, CP and CV of a gas of
diatomic molecules, A, are given (in units of
J mol–1 K–1) by 29 and 22, respectively.
Another gas of diatomic molecules, B, has the
corresponding values 30 and 21. If they are
treated as ideal gases, then :-
A.
A is rigid but B has a vibrational mode
B.
A has a vibrational mode but B has none
C.
A has one vibrational mode and B has two
D.
Both A and B have a vibrational mode each
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 9th April Evening Slot
A massless spring (k = 800 N/m), attached with
a mass (500 g) is completely immersed in 1 kg
of water. The spring is stretched by 2 cm and
released so that it starts vibrating. What would
be the order of magnitude of the change in the
temperature of water when the vibrations stop
completely ? (Assume that the water container
and spring receive negligible heat and specific
heat of mass = 400 J/kg K, specific heat of
water = 4184 J/kg K)
A.
10–3 K
B.
10–1 K
C.
10–5K
D.
10–4 K
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 9th April Evening Slot
Two materials having coefficients of thermal
conductivity '3K' and 'K' and thickness 'd' and
'3d', respectively, are joined to form a slab as
shown in the figure. The temperatures of the
outer surfaces are '$\theta $2' and '$\theta $1' respectively,
($\theta $2 > $\theta $1). The temperature at the interface is :-
A.
${{{\theta _1}} \over {10}} + {{9{\theta _2}} \over {10}}$
B.
${{{\theta _2} + {\theta _1}} \over 2}$
C.
${{{\theta _1}} \over {6}} + {{5{\theta _2}} \over {6}}$
D.
${{{\theta _1}} \over {3}} + {{2{\theta _2}} \over {3}}$
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 9th April Morning Slot
An HCl molecule has rotational, translational
and vibrational motions. If the rms velocity of
HCl molecules in its gaseous phase is $\overline v $ , m is
its mass and kB is Boltzmann constant, then its
temperature will be :
A.
${{m{{\overline v }^2}} \over {5{k_B}}}$
B.
${{m{{\overline v }^2}} \over {6{k_B}}}$
C.
${{m{{\overline v }^2}} \over {7{k_B}}}$
D.
${{m{{\overline v }^2}} \over {3{k_B}}}$
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 9th April Morning Slot
Following figure shows two processes A and
B for a gas. If $\Delta $QA and $\Delta $QB are the amount of
heat absorbed by the system in two cases, and
$\Delta $UA and $\Delta $UB are changes in internal energies,
respectively, then :
A.
$\Delta $QA > $\Delta $QB ; $\Delta $UA > $\Delta $UB
B.
$\Delta $QA < $\Delta $QB ; $\Delta $UA < $\Delta $UB
C.
$\Delta $QA > $\Delta $QB ; $\Delta $UA = $\Delta $UB
D.
$\Delta $QA = $\Delta $QB ; $\Delta $UA = $\Delta $UB
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 9th April Morning Slot
For a given gas at 1 atm pressure, rms speed
of the molecule is 200 m/s at 127°C. At 2 atm
pressure and at 227°C, the rms speed of the
molecules will be :
A.
100 m/s
B.
100 $\sqrt 5 $ m/s
C.
80 $\sqrt 5 $ m/s
D.
80 m/s
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 8th April Evening Slot
The temperature, at which the root mean square
velocity of hydrogen molecules equals their
escape velocity from the earth, is closest to :
[Boltzmann Constant kB = 1.38 × 10–23 J/K Avogadro Number NA = 6.02 × 1026 /kg Radius of Earth : 6.4 × 106 m Gravitational acceleration on Earth = 10ms–2]
[Boltzmann Constant kB = 1.38 × 10–23 J/K Avogadro Number NA = 6.02 × 1026 /kg Radius of Earth : 6.4 × 106 m Gravitational acceleration on Earth = 10ms–2]
A.
3 × 105 K
B.
104 K
C.
650 K
D.
800 K
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 8th April Evening Slot
The given diagram shows four processes i.e.,
isochoric, isobaric, isothermal and adiabatic.
The correct assignment of the processes, in the
same order is given by :-
A.
d a b c
B.
a d b c
C.
d a c b
D.
a d c b
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 8th April Morning Slot
Two identical beakers A and B contain equal
volumes of two different liquids at 60°C each
and left to cool down. Liquid in A has density
of 8 × 102 kg/m3 and specific heat of
2000 J kg–1 K–1 while liquid in B has density
of 103 kg m–3 and specific heat of
4000 J kg–1 K–1. Which of the following best
describes their temperature versus time graph
schematically? (assume the emissivity of both
the beakers to be the same)
A.
B.
C.
D.
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 8th April Morning Slot
A thermally insulated vessel contains 150g of
water at 0°C. Then the air from the vessel is
pumped out adiabatically. A fraction of water
turns into ice and the rest evaporates at 0°C
itself. The mass of evaporated water will be
closest to :
(Latent heat of vaporization of water
= 2.10 × 106 J kg–1 and Latent heat of Fusion
of water = 3.36 × 105 J kg–1)
A.
35 g
B.
130 g
C.
20 g
D.
150 g
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 12th January Evening Slot
An ideal gas is enclosed in a cylinder at pressure of 2 atm and temperature 300 K. The mean time between two successive collisions is 6 $ \times $ 10–8 s. If the pressure is doubled and temperature is increased to 500 K, the mean time between two successive collisions will be close to
A.
0.5 $ \times $ 10$-$8 s
B.
4 $ \times $ 10$-$8 s
C.
3 $ \times $ 10$-$6 s
D.
2 $ \times $ 10$-$7 s
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 12th January Evening Slot
A vertical closed cylinder is separated into two parts by a frictionless piston of mass m and of negligible thickness. The piston is free to move along the length of the cylinder. The length of the cylinder above the piston is $\ell $1, and that below the piston is $\ell $2, such that $\ell $1 > $\ell $2. Each part of the cylinder contains n moles of an ideal gas at equal temperature T. If the piston is stationary, its mass, m, will be given by :
(R is universal gas constant and g is the acceleration due to gravity)
(R is universal gas constant and g is the acceleration due to gravity)
A.
${{nRT} \over g}\left[ {{{{\ell _1} - {\ell _2}} \over {{\ell _1}{\ell _2}}}} \right]$
B.
${{RT} \over g}\left[ {{{2{\ell _1} + {\ell _2}} \over {{\ell _1}{\ell _2}}}} \right]$
C.
${{nRT} \over g}\left[ {{1 \over {{\ell _2}}} + {1 \over {{\ell _1}}}} \right]$
D.
${{RT} \over {ng}}\left[ {{{{\ell _1} - 3{\ell _2}} \over {{\ell _1}{\ell _2}}}} \right]$
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 12th January Morning Slot
For the given cyclic process CAB as shown for a gas, the work done is :
A.
1 J
B.
10 J
C.
5 J
D.
30 J
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 12th January Morning Slot
An ideal gas occupies a volume of 2m3 at a pressure of 3 $ \times $ 106 Pa. The energy of the gas is :
A.
6 $ \times $ 104 J
B.
9$ \times $ 106 J
C.
3 $ \times $ 102 J
D.
108 J
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 12th January Morning Slot
A cylinder of radius R is surrounded by a cylindrical shell of inner radius R and outer radius 2R. The thermal conductivity of the material of the inner cylinder is K1 and the of the outer cylinder is K2. Assuming no loss of heat, the effective thermal conductivity of the system for heat flowing along the length of the cylinder is :
A.
K1 + K2
B.
${{{K_1} + 3{K_2}} \over 4}$
C.
${{{K_1} + {K_2}} \over 2}$
D.
${{2{K_1} + 3{K_2}} \over 5}$
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 11th January Evening Slot
When 100 g of a liquid A at 100oC is added to 50 g of a liquid B at temperature 75oC, the temperature of the mixture becomes 90oC. The temperature of the mixture, if 100 g of liquid A at 100oC is added to 50 g of liquid B at 50oC, will be :
A.
60oC
B.
70oC
C.
85oC
D.
80oC
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 11th January Evening Slot
In a process, temperature and volume of one mole of an ideal monoatomic gas are varied according to the relation VT = K, where K is a constant. In this process the temperature of the gas is increased by $\Delta $T. The
amount of heat absorbed by gas is (R is gas constant) :
A.
${1 \over 2}$ KR$\Delta $T
B.
${1 \over 2}$ R$\Delta $T
C.
${3 \over 2}$ R$\Delta $T
D.
${2K \over 3}$ $\Delta $T
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 11th January Evening Slot
Two rods A and B of identical dimensions are at temperature 30°C. If A is heated upto 180oC and B upto ToC, then the new lengths are the same. If the ratio of the coefficients of linear expansion of A and B is 4 : 3, then the value of T is
A.
200oC
B.
270oC
C.
230oC
D.
250oC
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 11th January Evening Slot
A metal ball of mass 0.1 kg is heated upto 500oC and dropped into a vessel of heat capacity 800 JK–1 and containing 0.5 kg water. The initial temperature of water and vessel is 30oC. What is the approximate percentage increment in the temperature of the water? [Specific Heat Capacities of water and metal are, respectively, 4200 Jkg–1 and 400 Jkg–1 K–1
A.
20%
B.
25%
C.
15%
D.
30%
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 11th January Evening Slot
A thermometer graduated according to a linear scale reads a value x0 when in contact with boiling water, and x0/3 when in contact with ice. What is the temperature of an object in oC, if this thermometer in the contact with the object reads x0/2 ?
A.
60
B.
35
C.
25
D.
40
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 11th January Morning Slot
Ice at –20oC is added to 50 g of water at 40oC. When the temperature of the mixture reaches 0oC, it is found that 20 g of ice is still unmelted. The amount of ice added to the water was close to (Specific heat of water = 4.2J/g/oC Specific heat of Ice = 2.1J/g/oC Heat of fusion of water at 0oC= 334J/g)
A.
100 g
B.
60 g
C.
50 g
D.
40 g
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 11th January Morning Slot
A rigid diatomic ideal gas undergoes an adiabatic process at room temperature. The relation between temperature and volume for this process is TVx = constant, then x is :
A.
${5 \over 3}$
B.
${2 \over 5}$
C.
${3 \over 5}$
D.
${2 \over 3}$
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 11th January Morning Slot
A gas mixture consists of 3 moles of oxygen and 5 moles of argon at temperature T. considering only translational and rotational modes, the total internal energy of the system is :
A.
12 RT
B.
20 RT
C.
4 RT
D.
15 RT
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 10th January Evening Slot
An unknown metal of mass 192 g heated to a temperature of 100oC was immersed into a brass calorimeter of mass 128 g containing 240 g of water at a temperature of 8.4oC. Calculate the specific heat of the unknown metal if water temperature stabilizes at 21.5oC. (Specific heat of brass is 394 J kg–1 K–1)
A.
458 J kg–1 K–1
B.
1232 J kg–1 K–1
C.
654 J kg–1 K–1
D.
916 J kg–1 K–1
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 10th January Evening Slot
Half mole of an ideal monoatomic gas is heated at constant pressure of 1 atm from 20oC to 90oC. Work done
by gas is close to – (Gas constant R = 8.31 J/mol.K)
A.
581 J
B.
73 J
C.
146 J
D.
291 J
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 10th January Evening Slot
Two kg of a monoatomic gas is at a pressure of 4 $ \times $ 104 N/m2. The density of the gas is 8 kg/m3. What is the order of energy of the gas due to its thermal motion ?
A.
104 J
B.
103 J
C.
105 J
D.
106 J
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 10th January Morning Slot
A heat source at T = 103 K is connected to another heat reservoir at T = 102 K by a copper slab which is 1 mthick. Given that the thermal conductivity of copper is 0.1 WK–1m–1, the energy flux through it in the steady state is -
A.
200 Wm$-$2
B.
65 Wm$-$2
C.
120 Wm$-$2
D.
90 Wm$-$2
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 10th January Morning Slot
Three Carnot engines operate in series between a heat source at a temperature T1 and a heat sink at temperature T4 (see figure). There are two other reservoirs at temperature T2 and T3, as shown, with T1 > T2 > T3 > T4. The three engines are equally efficient if -
A.
T2 = (T13T4)1/4; T3 = (T1T43)1/4
B.
T2 = (T1T4)1/2; T3 = (T12T4)1/3
C.
T2 = (T1T42)1/3; T3 = (T12T4)1/3
D.
T2 = (T12T4)1/3; T3 = (T1T42)1/3
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 9th January Evening Slot
Two Carnot engines A and B are operated in series. The first one, A, receives heat at T1 (= 600 K) and rejects to a reservoir at temperature T2. The second engine B receives heat rejected by the first engine and, in tum, rejects to a heat reservoir at T3 (=400 K). Calculate the temperature T2 if the work outputs of the two engines are equal :
A.
600 K
B.
400 K
C.
300 K
D.
500 K
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 9th January Evening Slot
A 15 g mass of nitrogen gas is enclosed in a vessel at a temperature 27oC. Amount of heat transferred to the gas, so that rms velocity of molecules is doubled, is about : [Take R = 8.3 J/K mole]
A.
0.9 kJ
B.
6 kJ
C.
10 kJ
D.
14 kJ