2013
JEE Mains
MCQ
JEE Main 2013 (Offline)
The above $p$-$v$ diagram represents the thermodynamic cycle of an engine, operating with an ideal monatomic gas. The amount of heat, extracted from the source in a single cycle is
A.
${p_0}{v_0}$
B.
$\left( {{{13} \over 2}} \right){p_0}{v_0}$
C.
$\left( {{{11} \over 2}} \right){p_0}{v_0}$
D.
$4{p_0}{v_0}$
2013
JEE Mains
MCQ
JEE Main 2013 (Offline)
Assume that a drop of liquid evaporates by decreases in its surface energy, so that its temperature remains unchanged. What should be the minimum radius of the drop for this to be possible ? The surface tension is $T,$ density of liquid is $\rho $ and $L$ is its latent heat of vaporization.
A.
$\rho L/T$
B.
$\sqrt {T/\rho L} $
C.
$T/\rho L$
D.
$2T/\rho L$
2012
JEE Mains
MCQ
AIEEE 2012
Helium gas goes through a cycle $ABCD$ (consisting of two isochoric and isobaric lines) as shown in figure efficiency of this cycle is nearly : (Assume the gas to be close to ideal gas)
A.
$15.4\% $
B.
$9.1\% $
C.
$10.5\% $
D.
$12.5\% $
2012
JEE Mains
MCQ
AIEEE 2012
A Carnot engine, whose efficiency is $40\% $, takes in heat from a source maintained at a temperature of $500$ $K.$ It is desired to have an engine of efficiency $60\% .$ Then, the intake temperature for the same exhaust (sink) temperature must be :
A.
efficiency of Carnot engine cannot be made larger than $50\% $
B.
$1200$ $K$
C.
$750$ $K$
D.
$600$ $K$
2012
JEE Mains
MCQ
AIEEE 2012
A wooden wheel of radius $R$ is made of two semicircular part (see figure). The two parts are held together by a ring made of a metal strip of cross sectional area $S$ and length $L.$ $L$ is slightly less than $2\pi R.$ To fit the ring on the wheel, it is heated so that its temperature rises by $\Delta T$ and it just steps over the wheel. As it cools down to surrounding temperature, it process the semicircular parts together. If the coefficient of linear expansion of the metal is $\alpha $, and its Young's modulus is $Y,$ the force that one part of the wheel applies on the other part is :
A.
$2\pi SY\alpha \Delta T$
B.
$SY\alpha \Delta T$
C.
$\pi SY\alpha \Delta T$
D.
$2SY\alpha \Delta T$
2011
JEE Mains
MCQ
AIEEE 2011
A thermally insulated vessel contains an ideal gas of molecular mass $M$ and ratio of specific heats $\gamma .$ It is moving with speed $v$ and it's suddenly brought to rest. Assuming no heat is lost to the surroundings, Its temperature increases by:
A.
${{\left( {\gamma - 1} \right)} \over {2\gamma R}}M{v^2}K$
B.
${{\gamma {M^2}v} \over {2R}}K$
C.
${{\left( {\gamma - 1} \right)} \over {2R}}M{v^2}K$
D.
${{\left( {\gamma - 1} \right)} \over {2\left( {\gamma + 1} \right)R}}M{v^2}K$
2011
JEE Mains
MCQ
AIEEE 2011
Three perfect gases at absolute temperatures ${T_1},\,{T_2}$ and ${T_3}$ are mixed. The masses of molecules are ${m_1},{m_2}$ and ${m_3}$ and the number of molecules are ${n_1},$ ${n_2}$ and ${n_3}$ respectively. Assuming no loss of energy, the final temperature of the mixture is:
A.
${{{n_1}{T_1} + {n_2}{T_2} + {n_3}{T_3}} \over {{n_1} + {n_2} + {n_3}}}$
B.
${{{n_1}T_1^2 + {n_2}T_2^2 + {n_3}T_3^2} \over {{n_1}{T_1} + {n_2}{T_2} + {n_3}{T_3}}}$
C.
${{n_1^2T_1^2 + n_2^2T_2^2 + n_3^2T_3^2} \over {{n_1}{T_1} + {n_2}{T_2} + {n_3}{T_3}}}$
D.
${{\left( {{T_1} + {T_2} + {T_3}} \right)} \over 3}$
2011
JEE Mains
MCQ
AIEEE 2011
$100g$ of water is heated from ${30^ \circ }C$ to ${50^ \circ }C$. Ignoring the slight expansion of the water, the change in its internal energy is (specific heat of water is $4184$ $J/kg/K$):
A.
$8.4$ $kJ$
B.
$84$ $kJ$
C.
$2.1$ $kJ$
D.
$4.2$ $kJ$
2011
JEE Mains
MCQ
AIEEE 2011
A Carnot engine operating between temperatures ${{T_1}}$ and ${{T_2}}$ has efficiency ${1 \over 6}$. When ${T_2}$ is lowered by $62$ $K$ its efficiency increases to ${1 \over 3}$. Then ${T_1}$ and ${T_2}$ are, respectively:
A.
$372$ $K$ and $330$ $K$
B.
$330$ $K$ and $268$ $K$
C.
$310$ $K$ and $248$ $K$
D.
$372$ $K$ and $310$ $K$
2010
JEE Mains
MCQ
AIEEE 2010
A diatomic ideal gas is used in a Carnot engine as the working substance. If during the adiabatic expansion part of the cycle the volume of the gas increases from $V$ to $32$ $V$, the efficiency of the engine is
A.
$0.5$
B.
$0.75$
C.
$0.99$
D.
$0.25$
2009
JEE Mains
MCQ
AIEEE 2009
A long metallic bar is carrying heat from one of its ends to the other end under steady-state. The variation of temperature $\theta $ along the length $x$ of the bar from its hot end is best described by which of the following figures?
A.
B.
C.
D.
2009
JEE Mains
MCQ
AIEEE 2009
Statement - 1: The temperature dependence of resistance is usually given as $R = {R_0}\left( {1 + \alpha \,\Delta t} \right).$ The resistance of wire changes from $100\Omega $ to $150\Omega $ when its temperature is increased from ${27^ \circ }C$ to ${227^ \circ }C$. This implies that $\alpha = 2.5 \times {10^{ - 3}}/C.$
Statement - 2: $R = {R_0}\left( {1 + \alpha \,\Delta t} \right)$ is valid only when the change in the temperature $\Delta T$ is small and $\Delta T = \left( {R - {R_0}} \right) < < {R_0}.$
A.
Statement - 1 is true, Statement - 2 is true; Statement - 2 is the correct explanation of Statement - 1
B.
Statement - 1 is true, Statement - 2 is true; Statement - 2 is not the correct explanation of Statement - 1
C.
Statement - 1 is false, Statement - 2 is true
D.
Statement - 1 is true, Statement - 2 is false
2009
JEE Mains
MCQ
AIEEE 2009
One $kg$ of a diatomic gas is at a pressure of $8 \times {10^4}\,N/{m^2}.$ The density of the gas is $4kg/{m^3}$. What is the energy of the gas due to its thermal motion ?
A.
$5 \times {10^4}\,J$
B.
$6 \times {10^4}\,J$
C.
$7 \times {10^4}\,J$
D.
$3 \times {10^4}\,J$
2009
JEE Mains
MCQ
AIEEE 2009
Two moles of helium gas are taken over the cycle $ABCD,$ as shown in the $P$-$T$ diagram.
Assuming the gas to be ideal the work done on the gas in taking it from $A$ to $B$ is :
A.
$300$ $R$
B.
$400$ $R$
C.
$500$ $R$
D.
$200$ $R$
2009
JEE Mains
MCQ
AIEEE 2009
Two moles of helium gas are taken over the cycle $ABCD,$ as shown in the $P$-$T$ diagram.
The work done on the gas in taking it from $D$ to $A$ is :
A.
$+414$ $R$
B.
$-690$ $R$
C.
$+690$ $R$
D.
$-414$ $R$
2009
JEE Mains
MCQ
AIEEE 2009
Two moles of helium gas are taken over the cycle $ABCD$, as shown in the $P$-$T$ diagram.
The net work done on the gas in the cycle $ABCDA$ is:
A.
$276$ $R$
B.
$1076$ $R$
C.
$1904$ $R$
D.
zero
2008
JEE Mains
MCQ
AIEEE 2008
The speed of sound in oxygen $\left( {{O_2}} \right)$ at a certain temperature is $460\,\,m{s^{ - 1}}.$ The speed of sound in helium $(He)$ at the same temperature will be (assume both gases to be ideal)
A.
$1421\,\,m{s^{ - 1}}$
B.
$500\,\,m{s^{ - 1}}$
C.
$650\,\,m{s^{ - 1}}$
D.
$300\,\,m{s^{ - 1}}$
2008
JEE Mains
MCQ
AIEEE 2008
An insulated container of gas has two chambers separated by an insulating partition. One of the chambers has volume ${V_1}$ and contains ideal gas at pressure ${P_1}$ and temperature ${T_1}$. The other chamber has volume ${V_2}$ and contains ideal gas at pressure ${P_2}$ and temperature ${T_2}$. If the partition is removed without doing any work on the gas, the final equilibrium temperature of the gas in the container will be
A.
${{{T_1}{T_2}\left( {{P_1}{V_1} + {P_2}{V_2}} \right)} \over {{P_1}{V_1}{T_2} + {P_2}{V_2}{T_1}}}$
B.
${{{P_1}{V_1}{T_1} + {P_2}{V_2}{T_2}} \over {{P_1}{V_1} + {P_2}{V_2}}}$
C.
${{{P_1}{V_1}{T_2} + {P_2}{V_2}{T_1}} \over {{P_1}{V_1} + {P_2}{V_2}}}$
D.
${{{T_1}{T_2}\left( {{P_1}{V_1} + {P_2}{V_2}} \right)} \over {{P_1}{V_1}{T_1} + {P_2}{V_2}{T_2}}}$
2007
JEE Mains
MCQ
AIEEE 2007
If ${C_p}$ and ${C_v}$ denote the specific heats of nitrogen per unit mass at constant pressure and constant volume respectively, then
A.
${C_p} - {C_v} = 28R$
B.
${C_p} - {C_v} = R/28$
C.
${C_p} - {C_v} = R/14$
D.
${C_p} - {C_v} = R$
2007
JEE Mains
MCQ
AIEEE 2007
When a system is taken from state $i$ to state $f$ along the path iaf, it is found that $Q=50$ cal and $W=20$ $cal$. Along the path $ibf$ $Q=36$ $cal.$ $W$ along the path $ibf$ is
A.
$14$ $cal$
B.
$6$ $cal$
C.
$16$ $cal$
D.
$66$ $cal$
2007
JEE Mains
MCQ
AIEEE 2007
A Carnot engine, having an efficiency of $\eta = 1/10$ as heat engine, is used as a refrigerator . If the work done on the system is $10$ $J$, the amount of energy absorbed from the reservoir at lower temperature is
A.
$100$ $J$
B.
$99$ $J$
C.
$90$ $J$
D.
$1$ $J$
2007
JEE Mains
MCQ
AIEEE 2007
One end of a thermally insulated rod is kept at a temperature ${T_1}$ and the other at ${T_2}$. The rod is composed of two sections of length ${L_1}$ and ${L_2}$ and thermal conductivities ${K_1}$ and ${K_2}$ respectively. The temperature at the interface of the two section is
A.
${{\left( {{K_1}{L_1}{T_1} + {K_2}{L_2}{T_2}} \right)} \over {\left( {{K_1}{L_1} + {K_2}{L_2}} \right)}}$
B.
${{\left( {{K_2}{L_2}{T_1} + {K_1}{L_1}{T_2}} \right)} \over {\left( {{K_1}{L_1} + {K_2}{L_2}} \right)}}$
C.
${{\left( {{K_2}{L_1}{T_1} + {K_1}{L_2}{T_2}} \right)} \over {\left( {{K_2}{L_1} + {K_1}{L_2}} \right)}}$
D.
${{\left( {{K_1}{L_2}{T_1} + {K_2}{L_1}{T_2}} \right)} \over {\left( {{K_1}{L_2} + {K_2}{L_1}} \right)}}$
2006
JEE Mains
MCQ
AIEEE 2006
Assuming the Sun to be a spherical body of radius $R$ at a temperature of $TK$, evaluate the total radiant powered incident of Earth at a distance $r$ from the Sun
Where r0 is the radius of the Earth and $\sigma $ is Stefan's constant.
A.
$4\pi r_0^2{R^2}\sigma {{{T^4}} \over {{r^2}}}$
B.
$\pi r_0^2{R^2}\sigma {{{T^4}} \over {{r^2}}}$
C.
$r_0^2{R^2}\sigma {{{T^4}} \over {4\pi {r^2}}}$
D.
${R^2}\sigma {{{T^4}} \over {{r^2}}}$
2006
JEE Mains
MCQ
AIEEE 2006
The work of $146$ $kJ$ is performed in order to compress one kilo mole of gas adiabatically and in this process the temperature of the gas increases by ${7^ \circ }C.$ The gas is $\left( {R = 8.3J\,\,mo{l^{ - 1}}\,{K^{ - 1}}} \right)$
A.
diatomic
B.
triatomic
C.
a mixture of monoatomic and diatomic
D.
monoatomic
2006
JEE Mains
MCQ
AIEEE 2006
Two rigid boxes containing different ideal gases are placed on a table. Box A contains one mole of nitrogen at temperature ${T_0},$ while Box contains one mole of helium at temperature $\left( {{7 \over 3}} \right){T_0}.$ The boxes are then put into thermal contact with each other, and heat flows between them until the gases reach a common final temperature (ignore the heat capacity of boxes). Then, the final temperature of the gases, ${T_f}$ in terms of ${T_0}$ is
A.
${T_f} = {3 \over 7}{T_0}$
B.
${T_f} = {7 \over 3}{T_0}$
C.
${T_f} = {3 \over 2}{T_0}$
D.
${T_f} = {5 \over 2}{T_0}$
2005
JEE Mains
MCQ
AIEEE 2005
A system goes from $A$ to $B$ via two processes $I$ and $II$ as shown in figure. If $\Delta {U_1}$ and $\Delta {U_2}$ are the changes in internal energies in the processes $I$ and $II$ respectively, then
A.
relation between $\Delta {U_1}$ and $\Delta {U_2}$ can not be determined
B.
$\Delta {U_1} = \Delta {U_2}$
C.
$\Delta {U_2} < \Delta {U_1}$
D.
$\Delta {U_2} > \Delta {U_1}$
2005
JEE Mains
MCQ
AIEEE 2005
The figure shows a system of two concentric spheres of radii ${r_1}$ and ${r_2}$ are kept at temperatures ${T_1}$ and ${T_2}$, respectively. The radial rate of flow of heat in a substance between the two concentric spheres is proportional to
A.
$In\left( {{{{r_2}} \over {{r_1}}}} \right)$
B.
${{\left( {{r_2} - {r_1}} \right)} \over {\left( {{r_1}{r_2}} \right)}}$
C.
${\left( {{r_2} - {r_1}} \right)}$
D.
${{{r_1}{r_2}} \over {\left( {{r_2} - {r_1}} \right)}}$
2005
JEE Mains
MCQ
AIEEE 2005
The temperature-entropy diagram of a reversible engine cycle is given in the figure. Its efficiency is
A.
${1 \over 4}$
B.
${1 \over 2}$
C.
${2 \over 3}$
D.
${1 \over 3}$
2005
JEE Mains
MCQ
AIEEE 2005
A gaseous mixture consists of $16$ $g$ of helium and $16$ $g$ of oxygen. The ratio ${{Cp} \over {{C_v}}}$ of the mixture is
A.
$1.62$
B.
$1.59$
C.
$1.54$
D.
$1.4$
2004
JEE Mains
MCQ
AIEEE 2004
One mole of ideal monatomic gas $\left( {\gamma = 5/3} \right)$ is mixed with one mole of diatomic gas $\left( {\gamma = 7/5} \right)$. What is $\gamma $ for the mixture? $\gamma $ Denotes the ratio of specific heat at constant pressure, to that at constant volume
A.
$35/23$
B.
$23/15$
C.
$3/2$
D.
$4/3$
2004
JEE Mains
MCQ
AIEEE 2004
Time taken by a $836$ $W$ heater to heat one litre of water from $10{}^ \circ C$ to $40{}^ \circ C$ is
A.
$150$ $s$
B.
$100$ $s$
C.
$50$ $s$
D.
$200$ $s$
2004
JEE Mains
MCQ
AIEEE 2004
The temperature of the two outer surfaces of a composite slab, consisting of two materials having coefficients of thermal conductivity $K$ and $2K$ and thickness $x$ and $4x,$ respectively, are ${T_2}$ and ${T_1}\left( {{T_2} > {T_1}} \right).$ The rate of heat transfer through the slab, in a steady state is $\left( {{{A\left( {{T_2} - {T_1}} \right)K} \over x}} \right)f,$ with $f$ equal to
A.
${2 \over 3}$
B.
${1 \over 2}$
C.
$1$
D.
${1 \over 3}$
2004
JEE Mains
MCQ
AIEEE 2004
If the temperature of the sun were to increase from $T$ to $2T$ and its radius from $R$ to $2R$, then the ratio of the radiant energy received on earth to what it was previously will be
A.
$32$
B.
$16$
C.
$4$
D.
$64$
2004
JEE Mains
MCQ
AIEEE 2004
Which of the following statements is correct for any thermodynamic system ?
A.
The change in entropy can never be zero
B.
Internal energy and entropy and state functions
C.
The internal energy changes in all processes
D.
The work done in an adiabatic process is always zero,
2004
JEE Mains
MCQ
AIEEE 2004
Two thermally insulated vessels $1$ and $2$ are filled with air at temperatures $\left( {{T_1},{T_2}} \right),$ volume $\left( {{V_1},{V_2}} \right)$ and pressure $\left( {{P_1},{P_2}} \right)$ respectively. If the value joining the two vessels is opened, the temperature inside the vessel at equilibrium will be
A.
${T_1}{T_2}\left( {{P_1}{V_1} + {P_2}{V_2}} \right)/\left( {{P_1}{V_1}{T_2} + {P_2}{V_2}{T_1}} \right)$
B.
$\left( {{T_1} + {T_2}} \right)/2$
C.
${{T_1} + {T_2}}$
D.
${T_1}{T_2}\left( {{P_1}{V_1} + {P_2}{V_2}} \right)/\left( {{P_1}{V_1}{T_1} + {P_2}{V_2}{T_2}} \right)$
2003
JEE Mains
MCQ
AIEEE 2003
''Heat cannot by itself flow from a body at lower temperature to a body at higher temperature'' is a statement or consequence of :
A.
second law of thermodynamics
B.
conservation of momentum
C.
conservation of mass
D.
first law of thermodynamics
2003
JEE Mains
MCQ
AIEEE 2003
The earth radiates in the infra-red region of the spectrum. The spectrum is correctly given by
A.
Rayleigh Jeans law
B.
Planck's law of radiation
C.
Stefan's law of radiation
D.
Wien's law
2003
JEE Mains
MCQ
AIEEE 2003
Which of the following parameters does not characterize the thermodynamic state of mattter?
A.
Temperature
B.
Pressure
C.
Work
D.
Volume
2003
JEE Mains
MCQ
AIEEE 2003
A carnot engine takes $3 \times {10^6}$ cal. of heat from a reservoir at ${627^ \circ }C,$ and gives it to a sink at ${27^ \circ }C$. The work done by the engine is
A.
$4.2 \times {10^6}J$
B.
$8.4 \times {10^6}J$
C.
$16.8 \times {10^6}J$
D.
zero
2003
JEE Mains
MCQ
AIEEE 2003
During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio ${C_p}/{C_V}$ for the gas is
A.
${4 \over 3}$
B.
$2$
C.
${5 \over 3}$
D.
${3 \over 2}$
2002
JEE Mains
MCQ
AIEEE 2002
Which statement is incorrect?
A.
all reversible cycles have same efficiency
B.
reversible cycle has more efficiency than an irreversible one
C.
Cannot cycle is a reversible one
D.
Cannot cycle has the maximum efficiency in all cycles.
2002
JEE Mains
MCQ
AIEEE 2002
1 mole of a gas with $\gamma = 7/5$ is mixed with $1$ mole of a gas with $\gamma = 5/3,$ then the value of $\gamma $ for the resulting mixture is
A.
$7/5$
B.
$2/5$
C.
$3/2$
D.
$12/7$
2002
JEE Mains
MCQ
AIEEE 2002
Infrared radiation is detected by
A.
spectrometer
B.
pyrometer
C.
nanometer
D.
photometer
2002
JEE Mains
MCQ
AIEEE 2002
Which of the following is more close to a black body?
A.
black board paint
B.
green leaves
C.
black holes
D.
red roses
2002
JEE Mains
MCQ
AIEEE 2002
Heat given to a body which raises its temperature by ${1^ \circ }C$ is
A.
water equivalent
B.
thermal capacity
C.
specific heat
D.
temperature gradient
2002
JEE Mains
MCQ
AIEEE 2002
At what temperature is the $r.m.s$ velocity of a hydrogen molecule equal to that of an oxygen molecule at ${47^ \circ }C?$
A.
$80K$
B.
$-73$ $K$
C.
$3$ $K$
D.
$20$ $K$
2002
JEE Mains
MCQ
AIEEE 2002
If mass-energy equivalence is taken into account, when water is cooled to form ice, the mass of water should
A.
increase
B.
remain unchanged
C.
decrease
D.
first increase then decrease
2002
JEE Mains
MCQ
AIEEE 2002
Even Carnot engine cannot give $100\% $ efficiency because we cannot
A.
prevent radiation
B.
find ideal sources
C.
reach absolute zero temperature
D.
eliminate friction.
2002
JEE Mains
MCQ
AIEEE 2002
Two spheres of the same material have radii $1$ $m$ and $4$ $m$ and temperatures $4000$ $K$ and $2000$ $K$ respectively. The ratio of the energy radiated per second by the first sphere to that by the second is
A.
$1:1$
B.
$16:1$
C.
$4:1$
D.
$1:9$
2002
JEE Mains
MCQ
AIEEE 2002
Cooking gas containers are kept in a lorry moving with uniform speed. The temperature of the gas molecules inside will
A.
increase
B.
decrease
C.
remain same
D.
decrease for some, while increase for others