A metal metre scale that is accurate up to 0.5 mm is made at a temperature of $25^{\circ} \mathrm{C}$. The range of temperatures within which it can be used is (Coefficient of linear expansion of the metal $=10^{-5} /{ }^{\circ} \mathrm{C}$ )

A Carnot engine uses diatomic gas as a working substance. During the adiabatic expansion part of the cycle, if the volume of the gas becomes 32 times its initial volume, then the efficiency of the engine is

The ratio of the average translational kinetic energies of hydrogen and oxygen at the same temperature is

When ' $n$ ' identical mercury drops combine to form a single big drop

The temperature of a body shown by a faulty Celsius thermometer is $49^{\circ} \mathrm{C}$ and by a correct Fahrenheit thermometer is $122^{\circ} \mathrm{F}$. The correction to be applied to the faulty thermometer is

If the radiation emitted by a perfect radiator has maximum intensity at a wavelength of $2900 \mathop {\rm{A}}\limits^{\rm{o}}$, the intensity of radiation emitted by it is

(Stefan-Boltzmann's constant $=5.67 \times 10^{-8} \mathrm{Wm}^{-2} \mathrm{~K}^{-4}$ and Wein's constant $=2.9 \times 10^{-3} \mathrm{mK}$ )

The ratio of the work done, change in internal energy and heat absorbed when a diatomic gas expands at constant pressure is

If the temperature of a gas is increased from $127^{\circ} \mathrm{C}$ to $527^{\circ} \mathrm{C}$, then the rms speed of the gas molecules

The temperature at which the reading on Fahrenheit scale becomes $90 \%$ more than the reading on Celsius scale is

A rectangular ice box of total surface area of $1000 \mathrm{~cm}^2$ initially contains 1.5 kg of ice at $0^{\circ} \mathrm{C}$. If the thickness of the walls of the box is 2 mm and the temperature outside the box is $42^{\circ} \mathrm{C}$, then the mass of the ice remaining in the box after 160 minutes is

(Thermal conductivity of the material of the box $=10^{-2} \mathrm{Wm}^{-1} \mathrm{~K}^{-1}$ and latent heat of the fusion of ice $=336 \times 10^3 \mathrm{Jkg}^{-1}$ )

At constant pressure, equal amounts of heat are supplied to a monoatomic gas and a diatomic gas separately. The ratio of the increases in internal energies of the two gases is

If the rms speed of the molecules of a gas at a temperature of $77^{\circ} \mathrm{C}$ is $50 \mathrm{~ms}^{-1}$, then the rms speed of the same gas molecules at a temperature of $150.5^{\circ} \mathrm{C}$ is

To increase the length of a metal rod by $0.4 \%$ the temperature of the rod is to be increased by (Coefficient of linear expansion of the metal $\left.=20 \times 10^{-6}{ }^{\circ} \mathrm{C}^{-1}\right)$

The power of a refrigerator that can make 15 kg of ice at $0^{\circ} \mathrm{C}$ from water at $30^{\circ} \mathrm{C}$ in one hour is

Three moles of an ideal gas undergoes a cyclic process $A B C A$ as shown in the figure. The pressure, volume and absolute temperature at points $A, B$ and $C$ are respectively $\left(p_1, V_1, T_1\right),\left(p_2, 3 V_1, T_1\right)$ and $\left(p_2, V_1, T_2\right)$. Then, the total work done in the cycle $A B C A$ is ( $R=$ Universal gas constant).

The pressure of a mixture of 64 g of oxygen, 28 g of nitrogen and 132 g of carbon dioxide gases in a closed vessel is $p$. Under isothermal conditions if entire oxygen is removed from the vessel, the pressure of the mixture of remaining two gases is

A body cools from a temperature of $60^{\circ} \mathrm{C}$ to $50^{\circ} \mathrm{C}$ in 10 minutes and $50^{\circ} \mathrm{C}$ to $40^{\circ} \mathrm{C}$ in 15 minutes. The time taken in minutes for the body to cool from $40^{\circ} \mathrm{C}$ to $30^{\circ} \mathrm{C}$ is

When the temperature of a gas in a closed vessel is increased by $2.4^{\circ} \mathrm{C}$, its pressure increases by $0.5 \%$. The initial temperature of the gas is

A gas is suddenly compressed such that its absolute temperature is doubled. If the ratio of the specific heat capacities of the gas is 1.5 , then the percentage decrease in the volume of the gas is

If the heat required to increase the rms speed of 4 moles of a diatomic gas from $v$ to $\sqrt{3} v$ is 83.1 kJ , then the initial temperature of the gas is

(universal gas constant $=8.31 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}$ )

The length of a metal rod is 20 cm and its area of cross-section is $4 \mathrm{~cm}^2$. If one end of the rod is kept at a temperature of $100^{\circ} \mathrm{C}$ and the other end is kept in ice at $0^{\circ} \mathrm{C}$, then the mass of the ice melted in 7 minutes is (Thermal conductivity of the metal $=90 \mathrm{Wm}^{-1} \mathrm{~K}^{-1}$ and latent heat of fusion of ice $=336 \times 10^3 \mathrm{Jkg}^{-1}$ )

The heat required to convert 8 g of ice at a temperature of $-20^{\circ} \mathrm{C}$ to steam at $100^{\circ} \mathrm{C}$ is [specific heat capacity of ice $=2100 \mathrm{Jkg}^{-1} \mathrm{~K}^{-1}$, specific heat capacity of water $=4200 \mathrm{~J} \mathrm{~kg}^{-1} \mathrm{~K}^{-1}$, latent heat of fusion of ice $=336 \times 10^3 \mathrm{~J} \mathrm{~kg}^{-1}$ and latent heat of steam $\left.=2.268 \times 10^6 \mathrm{Jkg}^{-1}\right]$

Two moles of a gas at a temperature of $327^{\circ} \mathrm{C}$ expands adiabatically such that its volume increases by $700 \%$. If the ratio of the specific heat capacities of the gas is $\frac{4}{3}$, then the work done by the gas is (Universal gas constant $=8.3 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}$ )

The molar specific heat of a monoatomic gas at constant pressure is

(Universal gas constant $=8.3 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}$ )

Steam at $100^{\circ} \mathrm{C}$ is added to 150 g water to increase its temperature from $20^{\circ} \mathrm{C}$ to $40^{\circ} \mathrm{C}$. The total mass of the water at $40^{\circ} \mathrm{C}$ is (specific heat capacity of water $=1 \mathrm{cal} \mathrm{g}^{-1}{ }^{\circ} \mathrm{C}^{-1}$ and latent heat of steam $\left.=540 \mathrm{cal} \mathrm{g}^{-1}\right)$

A blacksmith fixes circular iron frame on the wooden wheel of a bullock cart. The diameter of wooden wheel and circular iron frame are 5.012 m and 5 m respectively at $27^{\circ} \mathrm{C}$. The temperature (in ${ }^{\circ} \mathrm{C}$ ) to which iron ring must be heated so as to fit the wooden wheel is

(Coefficient of linear expansion of iron $\left.=1.2 \times 10^{-5}{ }^{\circ} \mathrm{C}^{-1}\right)$

Two moles of triatomic gas $\left(\gamma=\frac{4}{3}\right)$ at temperature $327^{\circ} \mathrm{C}$ expands adiabatically such that its volume becomes 8 times its initial volume. Later the temperature of the gas is doubled in an isochoric process. The total work done in the two processes is

(Where, R is universal gas constant)

If the temperature of a gas is increased from $27^{\circ} \mathrm{C}$ to $159^{\circ} \mathrm{C}$, then the percentage increase in the rms speed of the gas molecules is

The Fahrenheit and Kelvin scales of temperature will have the same reading at a temperature of

If the ratio of densities of two substances is $5: 6$ and the ratio of their specific heat capacities is $3: 5$, then the ratio of heat energies required per unit volume so that the two substances can have same temperature rise is

In a process, the work done by the system is equal to the decrease in its internal energy. The process that the system undergoes is

N molecules each of mass $m$ of gas $A$ and 2 N molecules each of mass 2 m of gas $B$ are contained in a vessel which is maintained at a temperature $T$. The mean square velocity of the molecules of gas $B$ is denoted by $v_2^2$ and the mean square of the $x$-component velocity of the molecules of gas $A$ is denoted by $v_1^2$, then $v_1 / v_2$ is

The length of a metal rod at $30^{\circ} \mathrm{C}$ is 30 cm . If its temperature is raised to $105^{\circ} \mathrm{C}$, its length is increased by 0.027 cm . Then, the coefficient of linear expansion of the metal is

The heat energy required to convert 10 kg of ice at $-10^{\circ} \mathrm{C}$ into water at $0^{\circ} \mathrm{C}$ is (specific heat capacity of ice $=0.5 \mathrm{calg}^{-1}$ and latent heat of fusion of ice $=80 \mathrm{calg}^{-1}$ )

If the reading in Fahrenheit scale is twice the reading in Celsius scale, then the reading in Fahrenheit scale is

When some amount of heat energy is supplied to a monatomic gas, the percentage of heat energy used for increasing the internal energy of the gas $(\gamma=5 / 3)$ is

The average energy possessed by an oscillator at a temperature 300 K is (Boltzmann constant $=1.38 \times 10^{-23} \mathrm{JK}^{-1}$ )

For an ideal gas at a temperature of $27^{\circ} \mathrm{C}$ and at constant pressure, the coefficient of volume expansion is nearly

Air is filled at $60^{\circ} \mathrm{C}$ in a vessel of open mouth. The vessel is heated to a temperature $f^{\circ} \mathrm{C}$ so that $1 / 4$ th of the air is escaped from the vessel. Assuming air as ideal gas and the volume of the vessel remaining constant, then the value of $t$ is

The temperature of 100 g of water is to be raised from $24^{\circ} \mathrm{C}$ to $90^{\circ} \mathrm{C}$ by adding steam at $100^{\circ} \mathrm{C}$ to it. The mass of the steam required in this process is (latent heat of steam is $540 \mathrm{cal} \mathrm{g}^{-1}$ )

Two identical containers $A$ and $B$ with frictionless pistons contain the same ideal gas at the same temperature and same volume $V$. The mass of the gas in $A$ is $m_A$ and that in $B$ is $m_B$. The gas in each cylinder is now allowed to expand isothermally to the same final volume $2 V$. The changes in the pressure of the gases in $A$ and $B$ are found to be $2 \Delta p$ and $3 \Delta p$ respectively. Then the relation between $m_A$ and $m_B$ is

Two rod of same area of cross-section have lengths $L$ and $2 L$ and coefficients of linear expansions $2 \alpha$ and $a$ respectively. If they are welded to form a composite rod of length $3 L$ then the coefficient of linear expansion of the composite rod is

For a given mass of a gas at constant temperature, the volume and the pressure are $V$ and $p$ respectively. Then the slope of the graph drawn between $\log _e V$ on $X$-axis and $\log _e p$ on $Y$-axis is

An ideal gas at $127^{\circ} \mathrm{C}$ is compressed suddenly to $8 / 27 \mathrm{}$of its initial volume. If $\gamma=5 / 3$ for an ideal gas, then rise in its temperature is

An insulating cylinder contains 4 moles of an ideal diatomic gas. When a heat $Q$ is supplied to it, 2 moles of the gas molecules dissociate. If the temperature of the gas remains constant, then the value of $Q$ is ( $R=$ universal gas constant)

A circular copper ring at $30^{\circ} \mathrm{C}$ has a hole with an area of $9.98 \mathrm{~cm}^2$. It is made to slip onto a steel rod of cross-sectional area of $10 \mathrm{~cm}^2$, by raising the temperature of both ring and rod simultaneously by an amount $\Delta T$. If the coefficient of linear expansion of copper and steel are $17 \times 10^{-6} \rho \mathrm{C}$ and $11 \times 10^{-6} \rho \mathrm{C}$, then minimum value of $\Delta T$ should be

Statement I A device in which heat measurement can be made is called calorimeter.

Statement II Skating is possible on snow due to the formation of water below the skates. Water is formed due to the increase of temperature and ice melts.

Statement III Two bodies at different temperature are mixed in a calorimeter. Total internal energy of the two bodies remains conserved.

Which of the following is correct?

Which of the following statements is not true?

A gas system is taken through the thermodynamic cyclic process $1 \rightarrow 2 \rightarrow 3 \rightarrow 1$ as shown below. The amount of heat released by the system is

An ideal gas at pressure $p$ is enclosed in a container that is placed in a reservoir at temperature $T$. If the volume of the gas is increased to two times its original value, then the new pressure $p^{\prime}=$ $\_\_\_\_$ $p$

Two metal rods $A$ and $B$ each of length 50 cm can diameter 4.0 mm are joined together at temperature $30^{\circ} \mathrm{C}$. What is the change in length of the combined rod at $230^{\circ} \mathrm{C}$ ? (Given, linear expansion coefficients of rods $A$ and $B$ are respectively, $2.0 \times 10^{-5} /{ }^{\circ} \mathrm{C}$ and $1.0 \times 10^{-5} /{ }^{\circ} \mathrm{C}$ )

Find the difference in temperature between the water at the top and the bottom of 20 m high waterfall assuming 10\% of the energy of fall is spent in heating the water (use, specific heat capacity of water $=4000 \mathrm{~J} \mathrm{kg}^{-1} \mathrm{~K}^{-1}$ and $g=10 \mathrm{~m} / \mathrm{s}^2$ )

Assertion (A) The zeroth law of thermodynamics leads to the concept of temperature.

Reason (R) The zeroth law states that two systems in thermal equilibrium with a third system are in thermal equilibrium with each other.

The correct option among the following is

When a gas expands adiabatically, its volume is doubled while its absolute temperature is decreased by a factor of 2 . The value of the adiabatic constant is

An amount of 700 J of heat is transferred to a diatomic gas allowing it to expand with the pressure held constant. The work done on the gas is

176 g of $\mathrm{CO}_2$ can change its temperature from $0^{\circ} \mathrm{C}$ to $30^{\circ} \mathrm{C}$ by absorbing 3600 J of thermal energy. Molar specific heat of $\mathrm{CO}_2\left(\right.$ in $\left.\mathrm{J} \mathrm{mol}^{-1} \mathrm{~K}^{-1}\right)$ is

A solution consists of ether and 5.0 g of water at $0^{\circ} \mathrm{C}$. If the ether evaporates completely to freeze the water, then the mass of the ether in the solution is

Assertion (A) Heat and work are modes of energy transfer to a system resulting in change in its internal energy.

Reason (R) Heat and work in thermodynamics are state variables.

The correct option among the following is

An ideal gas at pressure $p_0$ undergoes an isothermal expansion until its volume is 8.0 times its initial volume. The gas is slowly and adiabatically compressed back to its original volume. If the adiabatic constant of the gas is $\gamma=\frac{4}{3}$, then the ratio of the average kinetic energy per molecule in this final state to that, in the initial state is

At what temperature is the root mean square rms speed of neon gas atoms is equal to the rms speed of helium gas atoms at $-33^{\circ} \mathrm{C}$ ?

(Atomic mass of $\mathrm{Ne}=20.2 \mathrm{u}$, and that of $\mathrm{He}=4.0 \mathrm{u}$ )

A piece of metal has a weight of 49 g in air and 39 g in a liquid of density $1.2 \times 10^3 \mathrm{~kg} / \mathrm{m}^3 \mathrm{kept}$ at $32^{\circ} \mathrm{C}$. When the temperature of the liquid is raised to $42^{\circ} \mathrm{C}$ the metal piece has a weight of 40 g . If the density of the liquid at $42^{\circ} \mathrm{C}$ is $1.0 \times 10^3 \mathrm{~kg} / \mathrm{m}^3$, then the coefficient of linear expansion of the metal is

A metal cooking pot has a base area of $0.2 \mathrm{~m}^2$ and thickness 2.0 cm . It boils water at a rate of $3.0 \mathrm{~kg} / \mathrm{min}$ when placed on a hot plate. The temperature of the part of the hot plate in contact with the pot is approximately [thermal conductivity of metal is $120 \mathrm{Js}^{-1} \mathrm{~m}^{-1} \mathrm{~K}^{-1}$, heat of vaporisation of water is $2 \times 10^6 \mathrm{~J} / \mathrm{kg}$ ]

A quantity of monoatomic gas undergoes a process in which pressure is changed linearly with volume. The pressure and volume are changed from initial value $\left(p_0 V_0\right)$ of final value $\left(3 p_0, 3 V_0\right)$. The heat absorbed by the gas during the process is

An ideal gas having initial pressure $p$, volume $V$ and temperature $T$ is allowed to expand adiabatically until its volume becomes 4 V , while its temperature falls to $\frac{T}{2}$. If the work done by the gas during the expansion is $\alpha p V$, the value of $\alpha$ is

At what temperature, an oxygen molecule has the same rms velocity as the hydrogen molecule has at 20 K ?

A hole of diameter 5 cm is drilled in a metal sheet at $30^{\circ} \mathrm{C}$. The linear expansion of metal is $2 \times 10^{-5} \mathrm{~K}^{-1}$. The diameter of the hole when the temperature is raised to $230^{\circ} \mathrm{C}$, is equal to

A metal cube absorbs 2100.0 J of heat when its temperature is raised by $2^{\circ} \mathrm{C}$. If the specific heat of the metal is $900 \mathrm{~J} \mathrm{~kg}^{-1} \mathrm{~K}^{-1}$, then the mass of the cube is

The net work done by an ideal gas going through the cycle as shown in the $p-V$ diagram below is

A diatomic gas $\left(C_p=\frac{7}{2} R\right)$ does 200 J of work when it is expanded isobarically. The heat given to the gas in the process is

Statement I Gas thermometers are less sensitive than liquid thermometers.

Statement II The ratio of universal gas constant and avogadro's number is called Boltzmann's constant.

Statement III The density of a given mass of a gas at constant pressure is inversely proportional to its absolute temperature.

The correct option among the following is

Find the ratio of the length of a steel rod and a copper rod, if the steel rod is 4 cm longer, then the copper rod at any temperature.

(The coefficient of linear expansion for steel and copper are $1.1 \times 10^{-5} /{ }^{\circ} \mathrm{C}$ and $1.7 \times 10^{-5} /{ }^{\circ} \mathrm{C}$, respectively)

An object cools from $100^{\circ} \mathrm{C}$ to $40^{\circ} \mathrm{C}$ in 10 min , when the surrounding temperature is $10^{\circ} \mathrm{C}$. Then the time taken by the object to cool from $70^{\circ} \mathrm{C}$ to $20^{\circ} \mathrm{C}$ is (take, $\ln 2=0.7, \ln 3=11, \ln 6=18$ )

1.00 kg of liquid water at $100^{\circ} \mathrm{C}$ undergoes a phase change into steam at $100^{\circ} \mathrm{C}$ at 1.0 atm (take it to be $1.00 \times 10^5 \mathrm{~Pa}$ ). The initial volume of the liquid water was $1.00 \times 10^{-3} \mathrm{~m}^3$ which is changed to $2.001 \mathrm{~m}^3$ of steam. Find the change in the internal energy of the system.

(Use heat of vaporisation $\simeq 2000 \mathrm{~kJ} / \mathrm{kg}$ )

A monoatomic gas does 100 J of work, when it is expanded isobarically. How much of heat is given to the gas in the process?

If the root mean square (rms) speed of nitrogen molecules at room temperature is $100 \mathrm{~m} / \mathrm{s}$, then the rms speed of helium molecule at the same temperature is

A sheet of steel at $20^{\circ} \mathrm{C}$ has size as shown in figure below. If the co-efficient of linear expansion for steel is $10^{-5}{ }^{\circ} \mathrm{C}^{-1}$, then what is the change in the area at $60^{\circ} \mathrm{C}$ ?

Different material of two identical long bars $A$ and $B$ are coated with wax and have their one end immersed in a hot oil bath. When the steady state is reached, the lengths for which wax melt are $l_A$ and $l_B$. If $k_A$ and $k_B$ are thermal conductivities of materials, then

A gas is at constant pressure $4 \times 10^5 \mathrm{~N} / \mathrm{m}^2$. When a heat energy of 2000 J is supplied to the gas, its volume changes by $3 \times 10^{-3} \mathrm{~m}^3$. What is the increase in its internal energy?

Certain amount of heat supplied to an ideal gas under isothermal condition will result in

If $\alpha_V$ and $T$ are the coefficient of volume expansion and temperature for an ideal gas respectively, then

If $\lambda$ denotes the wavelength at which the radiative emission from a black body at a temperature $T$ is maximum, then

A Carnot engine $C_1$ operates between temperature $T_1$ and $T_2\left(T_1>T_2\right)$. A second Carnot engine $C_2$ uses all the heat rejected by the engine $C_1$ and operates between temperature $T_2$ and $T_3$ (where $T_2>T_3$ ). The efficiency of this combined ( $C_1$ and $C_2$ together) engine is

All gases deviate from gas laws at

A solid of 2 kg mass absorbs 50 kJ when its temperature is raised from $20^{\circ} \mathrm{C}$ to $70^{\circ} \mathrm{C}$. The specific heat capacity of this solid in unit of $\mathrm{J} / \mathrm{kg}{ }^{\circ} \mathrm{C}$ is

A solid cylinder of radius $r_1=2.5 \mathrm{~cm}$, length $l_1=5.0 \mathrm{~cm}$ and temperature $40^{\circ} \mathrm{C}$ is suspended in an environment of temperature $60^{\circ} \mathrm{C}$. The thermal radiation transfer rate for cylinder is 1.0 W . If the cylinder is stretched until its radius becomes $r_2=0.50 \mathrm{~cm}$, the thermal radiation transfer rate is changed to

Five moles of an ideal gas has pressure $p_0$, volume $V_0$ and temperature $T_0$. The gas is expanded to volume $3 V_0$ along a path, so that the pressure $p$ is changed as function of volume $V$ as $p=p_0\left(V / V_0\right)$. The pressure is then reduced to $p_0$ maintaining the volume constant. The gas undergoes an isobaric compression till the volume and temperature become $V_0$ and $T_0$, respectively. The total work done by the gas during the entire process is

How many rotational degrees of freedom does a rigid diatomic molecule have?

The specific heat of helium at constant volume is 12.6 J $\mathrm{mol}^{-1} \mathrm{~K}^{-1}$. The specific heat of helium at constant pressure in $\mathrm{J} \mathrm{mol}^{-1} \mathrm{~K}^{-1}$ is approximately (assume, the universal gas constant, $R=8.314 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}$ )

A composite slab is prepared with two different materials $A$ and $B$. The relation between their coefficient of thermal conductivity and thickness is given as $K_A=\frac{K_B}{2}$ and $X_A=2 X_B$, respectively. If the temperature of faces of $A$ and $B$ are $75^{\circ} \mathrm{C}$ and $50^{\circ} \mathrm{C}$ respectively, what will be the temperature of common surface?

Work done on heating one mole of monoatomic gas adiabatically through $20^{\circ} \mathrm{C}$ is $W$. Then, the work done on heating 6 moles of rigid diatomic gas through the same change in temperature

If a gas has $n$ degrees of freedom, then the ratio of $\frac{C_p}{C_V}$ is