JEE Main 2024 — Thermodynamics

Choose the correct statement for processes $A$ & $B$ shown in figure. 

The efficiency of a Carnot engine operating between temperatures T₁ (source) and T₂ (sink) is:

A block of ice at $-10^{\circ}C$ is slowly heated and converted to steam at $100^{\circ}C$. Which of the following curves represent the phenomenon qualitatively:

The volume of an ideal gas $(\gamma=1.5)$ is changed adiabatically from 5 litres to 4 litres. The ratio of initial pressure to final pressure is:

Two vessels $A$ and $B$ are of the same size and are at same temperature. $A$ contains $1g$ of hydrogen and $B$ contains $1g$ of oxygen. ${P}_{A}$ and ${P}_{B}$ are the pressures of the gases in $A$ and $B$ respectively, then $\frac{{P}_{A}}{{P}_{B}}$ is :

During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio of $\frac{{C}_{p}}{{C}_{v}}$ for the gas is :

The specific heat at constant pressure of a real gas obeying $P V^2=R T$ equation is:

The average kinetic energy of a monatomic molecule is $0.414\mathrm{eV}$ at temperature: (Use ${K}_{B}=1.38\times {10}^{-23}J{\mathrm{mol}}^{-1}{K}^{-1}$)

$N$ moles of a polyatomic gas$(f=6)$ must be mixed with two moles of a monoatomic gas so that the mixture behaves as a diatomic gas. The value of $N$ is:

A diatomic gas $(\gamma =1.4)$ does $200J$ of work when it is expanded isobarically. The heat given to the gas in the process is :

A gas mixture consists of $8$ moles of argon and $6$ moles of oxygen at temperature $T$. Neglecting all vibrational modes, the total internal energy of the system is

If the root mean square velocity of hydrogen molecule at a given temperature and pressure is $2\mathrm{km}{s}^{-1},$ the root mean square velocity of oxygen at the same condition in $\mathrm{km}{s}^{-1}$ is:

The temperature of a gas is $-78^{\circ} \mathrm{C}$ and the average translational kinetic energy of its molecules is $\mathrm{K}$. The temperature at which the average translational kinetic energy of the molecules of the same gas becomes $2 \mathrm{~K}$ is :

A total of $48 \mathrm{~J}$ heat is given to one mole of helium kept in a cylinder. The temperature of helium increases by $2^{\circ} \mathrm{C}$. The work done by the gas is: Given, $\mathrm{R}=8.3 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$.

The resistances of the platinum wire of a platinum resistance thermometer at the ice point and steam point are $8 \Omega$ and $10 \Omega$ respectively. After inserting in a hot bath of temperature $400^{\circ} \mathrm{C}$, the resistance of platinum wire is :

At room temperature $\left(27^{\circ} \mathrm{C}\right)$, the resistance of a heating element is $50 \Omega$. The temperature coefficient of the material is $2.4 \times 10^{-4}{ }^{\circ} \mathrm{C}^{-1}$. The temperature of the element, when its resistance is $62 \Omega$, is _____ ${ }^{\circ} \mathrm{C}$.

Two conductors have the same resistances at $0^{\circ}C$ but their temperature coefficients of resistance are ${\alpha }_{1}$ and ${\alpha }_{2}$. The respective temperature coefficients for their series and parallel combinations are :

Energy of 10 non rigid diatomic molecules at temperature $T$ is :

The translational degrees of freedom $\left(f_t\right)$ and rotational degrees of freedom $\left(f_r\right)$ of $\mathrm{CH}_4$ molecule are:

A thermodynamic system is taken from an original state $A$ to an intermediate state $B$ by a linear process as shown in the figure. Its volume is then reduced to the original value from $B$ to $C$ by an isobaric process. The total work done by the gas from $A$ to $B$ and $B$ to $C$ would be : 

The total kinetic energy of $1$ mole of oxygen at $27^{\circ}C$ is : [Use universal gas constant $(R)=8.31J{\mathrm{mol}}^{-1}{K}^{-1}$ ]

Two different adiabatic paths for the same gas intersect two isothermal curves as shown in P-V diagram. The relation between the ratio $\frac{V_a}{V_d}$ and the ratio $\frac{V_b}{V_c}$ is: 

A sample of gas at temperature $T$ is adiabatically expanded to double its volume. Adiabatic constant for the gas is $\gamma=3 / 2$. The work done by the gas in the process is: $(\mu=1 \mathrm{~mole})$

If three moles of monoatomic gas $(\gamma =\frac{5}{3})$ is mixed with two moles of a diatomic gas $(\gamma =\frac{7}{5})$, the value of adiabatic exponent $\gamma$ for the mixture is:

A real gas within a closed chamber at $27^{\circ} \mathrm{C}$ undergoes the cyclic process as shown in figure. The gas obeys $P V^3=R T$ equation for the path $A$ to $B$. The net work done in the complete cycle is (assuming $R=8 \mathrm{~J} / \mathrm{mol} \mathrm{K}$ ): 

A sample of 1 mole gas at temperature $\mathrm{T}$ is adiabatically expanded to double its volume. If adiabatic constant for the gas is $\gamma=\frac{3}{2}$, then the work done by the gas in the process is:

A diatomic gas $(\gamma=1.4)$ does $100 \mathrm{~J}$ of work in an isobaric expansion. The heat given to the gas is :

P-T diagram of an ideal gas having three different densities $\rho_1, \rho_2, \rho_3$ (in three different cases) is shown in the figure. Which of the following is correct : 

The heat absorbed by a system in going through the given cyclic process is : 

The pressure and volume of an ideal gas are related as $P{V}^{\frac{3}{2}}=K$ (Constant). The work done when the gas is taken from state $A({P}_{1},{V}_{1},{T}_{1})$ to state $B({P}_{2},{V}_{2},{T}_{2})$ is :

The given figure represents two isobaric processes for the same mass of an ideal gas, then 

$0.08\mathrm{kg}$ air is heated at constant volume through $5^{\circ}C$. The specific heat of air at constant volume is $0.17\mathrm{kcal}{\mathrm{kg}}^{-1}^{\circ}{C}^{-1}$ and $1J=4.18\mathrm{joule}{\mathrm{cal}}^{-1}$. The change in its internal energy is approximately.

Given below are two statements : Statement (I) : The mean free path of gas molecules is inversely proportional to square of molecular diameter. Statement (II) : Average kinetic energy of gas molecules is directly proportional to absolute temperature of gas. In the light of the above statements, choose the correct answer from the options given below :

A mixture of one mole of monoatomic gas and one mole of a diatomic gas (rigid) are kept at room temperature $\left(27^{\circ} \mathrm{C}\right)$. The ratio of specific heat of gases at constant volume respectively is:

A sample contains mixture of helium and oxygen gas. The ratio of root mean square speed of helium and oxygen in the sample, is:

If $\mathrm{n}$ is the number density and $\mathrm{d}$ is the diameter of the molecule, then the average distance covered by a molecule between two successive collisions (i.e. mean free path) is represented by :

During an adiabatic process, if the pressure of a gas is found to be proportional to the cube of its absolute temperature, then the ratio of $\frac{C_{\mathrm{P}}}{\mathrm{C}_{\mathrm{V}}}$ for the gas is :

Two moles of a monoatomic gas is mixed with six moles of a diatomic gas. The molar specific heat of the mixture at constant volume is :

The parameter that remains the same for molecules of all gases at a given temperature is :

Two thermodynamical process are shown in the figure. The molar heat capacity for process $A$ and $B$ are ${C}_{A}$ and ${C}_{B}$. The molar heat capacity at constant pressure and constant volume are represented by ${C}_{P}$ and ${C}_{V}$, respectively. Choose the correct statement. 

At which temperature the r.m.s. velocity of a hydrogen molecule equal to that of an oxygen molecule at $47^{\circ}C$ ?

The temperature of a gas having $2.0\times {10}^{25}$ molecules per cubic meter at $1.38\mathrm{atm}$ (Given, $k=1.38\times {10}^{-23}J{K}^{-1})$ is :

If the collision frequency of hydrogen molecules in a closed chamber at $27^{\circ} \mathrm{C}$ is $\mathrm{Z}$, then the collision frequency of the same system at $127^{\circ} \mathrm{C}$ is :

On celcius scale the temperature of body increases by $40^{\circ} \mathrm{C}$. The increase in temperature on Fahrenheit scale is :

An ideal gas undergoes isothermal expansion at temperature T. If the volume doubles, by what factor does the pressure change?