JEE Main 2025 — Thermodynamics

A Carnot engine $(\mathrm{E})$ is working between two temperatures 473 K and 273 K . In a new system two engines - engine $E_1$ works between 473 K to 373 K and engine $E_2$ works between 373 K to 273 K . If $\eta_{12}, \eta_1$ and $\eta_2$ are the efficiencies of the engines $E, E_1$ and $E_2$, respectively, then

A container of fixed volume contains a gas at \(27^{\circ} \mathrm{C}\). To double the pressure of the gas, the temperature of gas should be raised to ______ \({ }^{\circ} \mathrm{C}\).

A cup of coffee cools from $90^{\circ} \mathrm{C}$ to $80^{\circ} \mathrm{C}$ in t minutes when the room temperature is $20^{\circ} \mathrm{C}$. The time taken by the similar cup of coffee to cool from $80^{\circ} \mathrm{C}$ to $60^{\circ} \mathrm{C}$ at the same room temperature is :

A gas is kept in a container having walls which are thermally non-conducting. Initially the gas has a volume of $800 \mathrm{~cm}^3$ and temperature $27^{\circ} \mathrm{C}$. The change in temperature when the gas is adiabatically compressed to $200 \mathrm{~cm}^3$ is : (Take $\gamma=1.5: \gamma$ is the ratio of specific heats at constant pressure and at constant volume)

A gun fires a lead bullet of temperature 300 K into a wooden block. The bullet having melting temperature of 600 K penetrates into the block and melts down. If the total heat required for the process is 625 J , then the mass of the bullet is $\qquad$ grams. (Latent heat of fusion of lead $=2.5 \times 10^4 \mathrm{JKg}^{-1}$ and specific heat capacity of lead $=125 \mathrm{JKg}^{-1}$ $\left.\mathrm{K}^{-1}\right)$

A monoatomic gas having $\gamma=\frac{5}{3}$ is stored in a thermally insulated container and the gas is suddenly compressed to $\left(\frac{1}{8}\right)^{\text {th }}$ of its initial volume. The ratio of final pressure and initial pressure is: ( $\gamma$ is the ratio of specific heats of the gas at constant pressure and at constant volume)

A wire of length 10 cm and diameter 0.5 mm is used in a bulb. The temperature of the wire is $1727^{\circ} \mathrm{C}$ and power radiated by the wire is 94.2 W. Its emissivity is $\frac{x}{8}$ where $x=$_______ (Given $\sigma=6.0 \times 10^{-8} \mathrm{~W} \mathrm{~m}^{-2} \mathrm{~K}^{-4}, \pi=3.14$ and assume that the emissivity of wire material is same at all wavelength.)

An amount of ice of mass $10^{-3} \mathrm{~kg}$ and temperature $-10^{\circ} \mathrm{C}$ is transformed to vapour of temperature $110^{\circ} \mathrm{C}$ by applying heat. The total amount of work required for this conversion is, (Take, specific heat of ice $=2100 \mathrm{Jkg}^{-1} \mathrm{~K}^{-1}$, specific heat of water $=4180 \mathrm{Jkg}^{-1} \mathrm{~K}^{-1}$, specific heat of steam $=1920 \mathrm{Jkg}^{-1} \mathrm{~K}^{-1}$, Latent heat of ice $=3.35 \times 10^5 \mathrm{Jkg}^{-1}$ and Latent heat of steam $=2.25 \times 10^6$ $\mathrm{Jkg}^{-1}$ )

An ideal gas exists in a state with pressure $P_0$ volume $\mathrm{V}_0$.It is isothermally expanded to 4 times of its initial volume $\left(\mathrm{V}_0\right)$, then isobarically compressed to its original volume. Finally the system is heated isochorically to bring it to its initial state. The amount of heat exchanged in this process is :

An ideal gas goes from an initial state to final state. During the process, the pressure of gas increases linearly with temperature. A. The work done by gas during the process is zero. B. The heat added to gas is different from change in its internal energy. C. The volume of the gas is increased. D. The internal energy of the gas is increased. E. The process is isochoric (constant volume process) Choose the correct answer from the options given below:

An ideal gas has undergone through the cyclic process as shown in the figure. Work done by the gas in the entire cycle is ______ $\times 10^{-1} \mathrm{~J}$. (Take $\pi=3.14$) 

An ideal gas initially at $0^{\circ} \mathrm{C}$ temperature, is compressed suddenly to one fourth of its volume. If the ratio of specific heat at constant pressure to that at constant volume is $3 / 2$, the change in temperature due to the thermodynamic process is _____ K.

$$ \text{Match the LIST-I with LIST-II} $$ \[ \begin{array}{|l|p{6cm}|l|p{4cm}|} \hline \textbf{LIST-I} & & \textbf{LIST-II} & \\ \hline A. & \text{Pressure varies inversely with volume of an ideal gas.} & I. & \text{Adiabatic process} \\ \hline B. & \text{Heat absorbed goes partly to increase internal energy and partly to do work.} & II. & \text{Isochoric process} \\ \hline C. & \text{Heat is neither absorbed nor released by a system.} & III. & \text{Isothermal process} \\ \hline D. & \text{No work is done on or by a gas.} & IV. & \text{Isobaric process} \\ \hline \end{array} \] $$ \text{Choose the correct answer from the options given below:} $$

Consider a rectangular sheet of solid material of length $\ell=9 \mathrm{~cm}$ and width $\mathrm{d}=4 \mathrm{~cm}$. The coefficient of linear expansion is $\alpha=3.1 \times 10^{-5} \mathrm{~K}^{-1}$ at room temperature and one atmospheric pressure. The mass of sheet $\mathrm{m}=0.1 \mathrm{~kg}$ and the specific heat capacity $\mathrm{C}_{\mathrm{v}}=900 \mathrm{~J} \mathrm{~kg}^{-1} \mathrm{~K}^{-1}$. If the amount of heat supplied to the material is $8.1 \times 10^2 \mathrm{~J}$ then change in area of the rectangular sheet is :-

During the melting of a slab of ice at 273 K at atmospheric pressure :

For a diatomic gas, if $\gamma_1=\left(\frac{C p}{C v}\right)$ for rigid molecules and $\gamma_2=\left(\frac{C p}{C v}\right)$ for another diatomic molecules, but also having vibrational modes. Then, which one of the following options is correct ? (Cp and Cv are specific heats of the gas at constant pressure and volume)

For a particular ideal gas which of the following graphs represents the variation of mean squared velocity of the gas molecules with temperature?

Given are statements for certain thermodynamic variables, (A) Internal energy, volume (V) and mass (M) are extensive variables. (B) Pressure (P), temperature (T) and density ( $\rho$ ) are intensive variables. (C) Volume (V), temperature (T) and density ( $\rho$ ) are intensive variables. (D) Mass (M), temperature (T) and internal energy are extensive variables. Choose the correct answer from the options given below :

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : With the increase in the pressure of an ideal gas, the volume falls off more rapidly in an isothermal process in comparison to the adiabatic process. Reason (R) : In isothermal process, $\mathrm{PV}=$ constant, while in adiabatic process $\mathrm{PV}^\gamma=$ constant. Here $\gamma$ is the ratio of specific heats, P is the pressure and V is the volume of the ideal gas. In the light of the above statements, choose the correct answer from the options given below :

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : In an insulated container, a gas is adiabatically shrunk to half of its initial volume. The temperature of the gas decreases. Reason (R): Free expansion of an ideal gas is an irreversible and an adiabatic process. In the light of the above statements, choose the correct answer from the options given below :

Identify the characteristics of an adiabatic process in a monoatomic gas. (A) Internal energy is constant. (B) Work done in the process is equal to the charge in internal energy. (C) The product of temperature and volume is a constant. (D) The product of pressure and volume is a constant. (E) The work done to change the temperature from $\mathrm{T}_1$ to $\mathrm{T}_2$ is proportional to $\left(\mathrm{T}_2-\mathrm{T}_1\right)$ Choose the correct answer from the options given below :

In an adiabatic process, which of the following statements is true?

$\gamma_{\mathrm{A}}$ is the specific heat ratio of monoatomic gas A having 3 translational degrees of freedom. $\gamma_B$ is the specific heat ratio of polyatomic gas B having 3 translational, 3 rotational degrees of freedom and 1 vibrational mode. If $\frac{\gamma_{\mathrm{A}}}{\gamma_{\mathrm{B}}}=\left(1+\frac{1}{\mathrm{n}}\right)$, then the value of $n$ is _______.

 Using the given $\mathrm{P}-\mathrm{V}$ diagram, the work done by an ideal gas along the path ABCD is :

 A poly-atomic molecule ( $C_V=3 R, C_P=4 R$, where $R$ is gas constant) goes from phase space point $\mathrm{A}\left(\mathrm{P}_{\mathrm{A}}=10^5 \mathrm{~Pa}, \mathrm{~V}_{\mathrm{A}}=4 \times 10^{-6} \mathrm{~m}^3\right)$ to point $\mathrm{B}\left(\mathrm{P}_{\mathrm{B}}=5 \times 10^4 \mathrm{~Pa}, \mathrm{~V}_{\mathrm{B}}=6 \times 10^{-6} \mathrm{~m}^3\right)$ to point $\mathrm{C}\left(\mathrm{P}_{\mathrm{C}}=10^4\right.$ $\left.\mathrm{Pa}, \mathrm{V}_{\mathrm{C}}=8 \times 10^{-6} \mathrm{~m}^3\right)$. A to B is an adiabatic path and $B$ to $C$ is an isothermal path. The net heat absorbed per unit mole by the system is :

Match List-I with List-II. \(\begin{array}{|l|l|l|l|} \hline & \text{List - I} & & \text{List - II} \\ \hline \text { (A) } & \text { Isobaric } & \text { (I) } & \Delta Q=\Delta W \\ \hline \text { (B) } & \text { Isochoric } & \text { (II) } & \Delta Q=\Delta U \\ \hline \text { (C) } & \text { Adiabatic } & \text { (III) } & \Delta Q=\text { zero } \\ \hline \text { (D) } & \text { Isothermal } & \text { (IV) } & \Delta Q=\Delta U+P \Delta V \\ \hline \end{array}\) $\Delta \mathrm{Q}=$ Heat supplied $\Delta \mathrm{W}=$ Work done by the system $\Delta \mathrm{U}=$ Change in internal energy $\mathrm{P}=$ Pressure of the system $\Delta \mathrm{V}=$ Change in volume of the system Choose the correct answer from the options given below:

Match List-I with List-II. $\begin{array}{|l|l|l|l|} \hline & \text{List-I} & & \text{List-II} \\ \hline \text{(A)} & \text{Isothermal} & \text{(I)} & \Delta \mathrm{W} \text{(work done)} =0 \\ \hline \text{(B)} & \text{Adiabatic} & \text{(II)} & \Delta \mathrm{Q} \text{(supplied heat)} =0 \\ \hline \text{(C)} & \text{Isobaric} & \text{(III)} & \begin{array}{l}\Delta \mathrm{U} \text{(change in internal} \\ \text{energy} \neq 0\end{array} \\ \hline \text{(D)} & \text{Isochoric} & \text{(IV)} & \Delta \mathrm{U}=0 \\ \hline\end{array}$ Choose the correct answer from the options given below :

Match the $\mathrm {List-I}$ with $\mathrm {List-II}$ $\begin{array}{|l|l|l|l|}\hline & \text{List-I} & & \text{List-II} \\ \hline \text{A.} & \text{Triatomic rigid gas} & \text{I.} & \frac{\mathrm{C}_{\mathrm{P}}}{\mathrm{C}_{\mathrm{V}}}=\frac{5}{3} \\ \hline \text{B.} & \begin{array}{l} \text{Diatomic non-rigid} \\ \text{gas} \end{array} & \text{II.} & \frac{\mathrm{C}_{\mathrm{P}}}{\mathrm{C}_{\mathrm{V}}}=\frac{7}{5} \\ \hline \text{C.} & \text{Monoatomic gas} & \text{III.} & \frac{\mathrm{C}_{\mathrm{P}}}{\mathrm{C}_{\mathrm{V}}}=\frac{4}{3} \\ \hline \text{D.} & \text{Diatomic rigid gas} & \text{IV }& \frac{\mathrm{C}_{\mathrm{P}}}{\mathrm{C}_{\mathrm{V}}}=\frac{9}{7} \\ \hline\end{array}$ Choose the $\mathrm {correct}$ answer from the options given below :

Pressure of an ideal gas, contained in a closed vessel, is increased by $0.4 \%$ when heated by $1^{\circ} \mathrm{C}$. Its initial temperature must be :

The helium and argon are put in the flask at the same room temperature ( 300 K). The ratio of average kinetic energies (per molecule) of helium and argon is : (Give : Molar mass of helium $=4 \mathrm{~g} / \mathrm{mol}$, Molar mass of argon $=40 \mathrm{~g} / \mathrm{mol}$)

The internal energy of air in $4 \mathrm{~m} \times 4 \mathrm{~m} \times 3 \mathrm{~m}$ sized room at 1 atmospheric pressure will be _______ $\times 10^6 \mathrm{~J}$. (Consider air as diatomic molecule)

The kinetic energy of translation of the molecules in 50 g of $\mathrm{CO}_2$ gas at $17^{\circ} \mathrm{C}$ is

The magnitude of heat exchanged by a system for the given cyclic process ABCA (as shown in figure) is (in SI unit) : 

The mean free path and the average speed of oxygen molecules at 300 K and 1 atm are $3 \times 10^{-7} \mathrm{~m}$ and $600 \mathrm{~m} / \mathrm{s}$ respectively. Find the frequency of its collisions.

The ratio of vapour densities of two gases at the same temperature is $\frac{4}{25}$, then the ratio of r.m.s. velocities will be:

The temperature of 1 mole of an ideal monoatomic gas is increased by $50^{\circ} \mathrm{C}$ at constant pressure. The total heat added and change in internal energy are $E_1$ and $E_2$, respectively. If $\frac{E_1}{E_2}=\frac{x}{9}$ then the value of $x$ is _____

The temperature of a body in air falls from $40^{\circ} \mathrm{C}$ to $24^{\circ} \mathrm{C}$ in 4 minutes. The temperature of the air is $16^{\circ} \mathrm{C}$. The temperature of the body in the next 4 minutes will be:

The workdone in an adiabatic change in an ideal gas depends upon only :

There are two vessels filled with an ideal gas where volume of one is double the volume of other. The large vessel contains the gas at 8 kPa at 1000 K while the smaller vessel contains the gas at 7 kPa at 500 K. If the vessels are connected to each other by a thin tube allowing the gas to flow and the temperature of both vessels is maintained at 600 K , at steady state the pressure in the vessels will be (in kPa).

Three conductors of same length having thermal conductivity $\mathrm{k}_1, \mathrm{k}_2$ and $\mathrm{k}_3$ are connected as shown in figure.  Area of cross sections of $1^{\text {st }}$ and $2^{\text {nd }}$ conductor are same and for $3^{\text {rd }}$ conductor it is double of the $1^{\text {st }}$ conductor. The temperatures are given in the figure. In steady state condition, the value of $\theta$ is _______ ${ }^{\circ} \mathrm{C}$. (Given : $\mathrm{k}_1=60 \mathrm{Js}^{-1} \mathrm{~m}^{-1} \mathrm{~K}^{-1}, \mathrm{k}_2=120 \mathrm{Js}^{-1} \mathrm{~m}^{-1} \mathrm{~K}^{-1}, \mathrm{k}_3=135 \mathrm{Js}^{-1} \mathrm{~m}^{-1} \mathrm{~K}^{-1}$ )

Two cylindrical rods A and B made of different materials, are joined in a straight line. The ratio of lengths, radii and thermal conductivities of these rods are : $\frac{\mathrm{L}_{\mathrm{A}}}{\mathrm{L}_{\mathrm{B}}}=\frac{1}{2}, \frac{\mathrm{r}_{\mathrm{A}}}{\mathrm{r}_{\mathrm{B}}}=2$ and $\frac{\mathrm{K}_{\mathrm{A}}}{\mathrm{K}_{\mathrm{B}}}=\frac{1}{2}$. The free ends of rods A and B are maintained at $400 \mathrm{~K}, 200 \mathrm{~K}$, respectively. The temperature of rods interface is ________ K, when equilibrium is established.

Two spherical bodies of same materials having radii 0.2 m and 0.8 m are placed in same atmosphere. The temperature of the smaller body is 800 K and temperature of the bigger body is 400 K . If the energy radiated from the smaller body is E, the energy radiated from the bigger body is (assume, effect of the surrounding temperature to be negligible),

Water falls from a height of 200 m into a pool. Calculate the rise in temperature of the water assuming no heat dissipation from the water in the pool. $\left(\right.$ Take $g=10 \mathrm{~m} / \mathrm{s}^2$, specific heat of water $\left.=4200 \mathrm{~J} /(\mathrm{kg} \mathrm{K})\right)$

Water of mass $m$ gram is slowly heated to increase the temperature from $T_1$ to $T_z$ The change in entropy of the water, given specific heat of water is $1 \mathrm{Jkg}^{-1} \mathrm{~K}^{-1}$, is :

Which of the following figure represents the relation between Celsius and Fahrenheit temperatures ?