Heat & Thermodynamics — JEE Main PYQs

Two rods A and B of identical dimensions are at temperature $30^{\circ }\mathrm{C}$. If a heated upto $180^{\circ }\mathrm{C}$ and B upto ${\mathrm{T}}^{\circ }\mathrm{C}$, then the new lengths are the same. If the ratio of the coefficients of linear expansion of $A$ and $B$ is …

In a process, temperature and volume of one mole of an ideal monoatomic gas are varied according to the relation $\mathrm{VT}=\mathrm{K}$, 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 g …

When 100 g of a liquid A at $100^{\circ }\mathrm{C}$ is added to 50 g of a liquid B at temperature $75^{\circ }\mathrm{C}$, the temperature of the mixture becomes $90^{\circ }\mathrm{C}$. The temperature of the mixture, if 100 g of liquid A at $100^{\circ }\mathrm{C}$ is added to …

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? ( $\mathrm{R}=8.3\mathrm{J}/\mathrm{mol}\mathrm{K}$ )

When ${\mathrm{M}}_1$ gram of ice at $-10^{\circ }\mathrm{C}$ (specific heat $=0.5\mathrm{cal}{\mathrm{g}}^{-1\circ }{\mathrm{C}}^{-1}$ ) is added to ${\mathrm{M}}_2$ gram of water at $50^{\circ }\mathrm{C}$, finally no ice is left and the water is at $0^{\circ }\mathrm{C}$. The v …

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 …

One mole of an ideal gas passes through a process where pressure and volume obey the relation $P=P_o\left[1-\frac{1}{2}{\left(\frac{V_o}{V}\right)}^2\right]$. Here $P_o$ and $V_o$ are constants. Calculate the change in the temperature of the gas if its volume change from …

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 constant pressure is

Ice at $-20^{\circ }\mathrm{C}$ is added to 50 g of water at $40^{\circ }\mathrm{C}$. When the temperature of the mixture reaches $0^{\circ }\mathrm{C}$, 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 wate …

A gas mixture consists of 3 moles of oxygen and 5 moles or argon at temperature T . Considering only translational and rotational modes, the total internal energy of the system is:

A rigid diatomic ideal gas undergoes an adiabatic process at room temperature. The rational between temperature and volume for the process is TV ${}^{\mathrm{x}}=$ constant, then x is:

An ideal gas occupies a volume of $2{\mathrm{m}}^3$ at a pressure of $3\times 10^6\mathrm{Pa}$. The energy of the gas is:

For the given cyclic process CAB as shown for a gas, the work done is:

A cylinder of radius R is surrounded by a cylindrical shell of inner radius R and outer radius 2 R . The thermal conductivity of the material of the inner cylinder is ${\mathrm{K}}_1$ and that of the outer cylinder is ${\mathrm{K}}_2$. Assuming no loss of heat, the effective …

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 Carnot engine has an efficiency of $1/6$. When the temperature of the sink is reduced by $62^{\circ }\mathrm{C}$, its efficiency is doubled. The temperatures of the source and the sink are, respectively

The number density of molecules of a gas depends on their distance $r$ from the origin as, $n(r)=n_0{e}^{-\alpha r^4}$. Then the total number of molecules is proportional to :

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 c …

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 ${\mathrm{l}}_1$, and that below the piston is …

The specific heats, $C_P$ and $C_V$ of a gas of diatomic molecules, A, are given (in units of J ${\mathrm{mol}}^{-1}{\mathrm{K}}^{-1}$) 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, t …

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 temperat …

Two Carnot engines A and B are operated in series. The first one, A, receives heat at ${\mathrm{T}}_1(=600\mathrm{K})$ and rejects to a reservoir at temperature ${\mathrm{T}}_2$. The second engine B receives heat rejected by the first engine and, in turns, rejects to a heat …

A 15 g mass of nitrogen gas is enclosed in a vessel at a temperature $27^{\circ }\mathrm{C}$. Amount of heat transferred to the gas, so that rms velocity of molecules is doubled, is about: [Take $\mathrm{R}=8.3\mathrm{J}/\mathrm{K}$ mole]

A mixture of 2 moles of helium gas (atomic mass $=4\mathrm{u}$), and 1 mole of argon gas (atomic mass $=40\mathrm{u}$) is kept at 300 K in a container. The ratio of their rms speeds …

Temperature difference of $120^{\circ }\mathrm{C}$ is maintained between two ends of a uniform rod AB of length 2L. Another bent rod PQ, of same cross-section as AB and length $\frac{3L}{2}$, is connected across AB (See figure). In steady state, temperature difference between …

A gas can be taken from A to B via two different processes ACB and ADB. When path ACB is used 60 J of heat flows into the system and 30 J of work is done by the system. If path ADB is used work done by the system is 10 J. The heat flow into the system in path ADB is

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 $20^{\circ }\mathrm{C}$ is: [Given that $\mathrm{R}=8.31\mathrm{J}{\mathrm{mol}}^{-1}{\mathrm{K}}^{-1}$]

n-moles of an ideal gas with constant volume heat capacity ${\mathrm{C}}_{\mathrm{V}}$ undergo an isobaric expansion by certain volume. The ratio of the work done in the process, to the heat supplied is

A $25\times 10^{-3}{\mathrm{m}}^3$ volume cylinder is filled with 1 mol of ${\mathrm{O}}_2$ gas at room temperature ( 300 K ). The molecular diameter of ${\mathrm{O}}_2$, and its root mean square speed, are found to be 0.3 nm and $200\mathrm{m}/\mathrm{s}$, respect …

Two moles of an ideal monoatomic gas occupies a volume V at $27^{\circ }$C. The gas expands adiabatically to a volume 2V. Calculate (a) the final temperature of the gas and (b) change in its internal energy.

The temperature of an open room of volume $30{\mathrm{m}}^3$ increases from $17^{\circ }\mathrm{C}$ to $27^{\circ }\mathrm{C}$ due to the sunshine. The atmospheric pressure in the room remains $1\times 10^5\mathrm{Pa}$. If ${\mathrm{n}}_i$ and ${\mathrm{n}}_f$ are the numb …

$C_p$ and $C_v$ are specific heats at constant pressure and constant volume respectively. It is observed that
$C_p-C_v=a$ for hydrogen gas
$C_p-C_v=b$ for nitrogen gas
The correct relation between a and b is:

A copper ball of mass 100 gm is at a temperature T. It is dropped in a copper calorimeter of mass 100 gm, filled with 170 gm of water at room temperature. Subsequently, the temperature of the system is found to be $75^{\circ }C$. T is given by: (Given: room temperature …

'n' moles of an ideal gas undergoes a process $A\to B$ as shown in the figure. The maximum temperature of the gas during the process will be :

A pendulum clock loses 12 s a day if the temperature is $40^{\circ }\mathrm{C}$ and gains 4 s a day if the temperature is $20^{\circ }\mathrm{C}$. The temperature at which the clock will show correct time, and the co-efficient of linear expansion ($\alpha$) of the metal of …

An ideal gas undergoes a quasi static, reversible process in which its molar heat capacity C remains constant. If during this process the relation of pressure P and volume V is given by ${\mathrm{PV}}^{\mathrm{n}}=$ constant, then n is given by (Here ${\mathrm{C}}_{\mathrm{P}}$ and …

Consider a spherical shell of radius R at temperature T . The black body radiation inside it can be considered as an ideal gas of photons with internal energy per unit volume $u=\frac{U}{V}\propto T^4$ and pressure …

Consider an ideal gas confined in an isolated closed chamber. As the gas undergoes an adiabatic expansion the average time of collision between molecules increases as ${\mathrm{V}}^{\mathrm{q}}$, where V is the volume of the gas. The value of q is : …

A solid body of constant heat capacity $1\mathrm{J}/{}^{\circ }\mathrm{C}$ is being heated by keeping it in contact with reservoirs in two ways:
(i) Sequentially keeping in contact with 2 reservoirs such that each reservoir supplies same amount of heat.
(ii) Sequentially keep …

The pressure that has to be applied to the ends of a steel wire of length 10 cm to keep its length constant when its temperature is raised by $100^{\circ }\mathrm{C}$ is :
(For steel Young's modulus is $2\times 10^{11}\mathrm{N}{\mathrm{m}}^{-2}$ and coefficient of thermal exp …

An open glass tube is immersed in mercury in such a way that a length of 8 cm extends above the mercury level. The open end of the tube is then closed and sealed and the tube is raised vertically up by additional 46 cm. What will be length of the air column above mercury in the t …

One mole of diatomic ideal gas undergoes a cyclic process ABC as shown in figure. The process BC is adiabatic. The temperatures at A, B and C are 400 K, 800 K and 600 K respectively. Choose the correct statement:

Three rods of Copper, Brass and Steel are welded together to from a Y-shaped structure. Area of cross section of each rod $=4{\mathrm{cm}}^2$. End of copper rod is maintained at $100^{\circ }\mathrm{C}$ where as ends of brass and steel are kept at $0^{\circ }\mathrm{C}$. Lengths o …

The above p-v diagram represents the thermodynamic cycle of an engine, operating with an ideal monoatomic gas. The amount of heat extracted from the source in a single cycle is

If a piece of metal is heated to temperature $\theta$ and then allowed to cool in a room which is at temperature ${\theta }_0$ the graph between the temperature T of the metal and time t will be closest to :

A wooden wheel of radius $R$ is made of two semicircular parts (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 $2\pi \mathrm{R}$. To fit the ring on the wheel, it is heated so that …

Helium gas goes through a cycle ABCDA (consisting of two isochoric and two isobaric lines) as shown in figure. Efficiency of this cycle is nearly: (Assume the gas to be close to ideal gas)

A liquid in a beaker has temperature $\theta (\mathrm{t})$ at time t and ${\theta }_0$ is temperature of surroundings, then according to Newton's law of cooling the correct graph between ${\log }_{\mathrm{e}}\left(\theta -{\theta }_0\right)$ and t is

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 thermally insulated vessel contains an ideal gas of molecular mass M and ratio of specific heats $\gamma$. It is moving with speed $v$ and is suddenly brought to rest. Assuming no heat is lost to the surroundings, its temperature increases by :