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The parameter that remains the same for molecules of all gases at a given temperature 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 \(\displaystyle \frac{C_P}{C_V} \) for the gas is:

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

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

Energy of \( 10 \) non rigid diatomic molecules at temperature \( T \) is:

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

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

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

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

A sample of \( 1 \) mole gas at temperature \( T \) 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:

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:

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

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

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

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 \( \frac{C_p}{C_v} \) for the gas is:

The specific heat at constant pressure of a real gas obeying \( PV^{2}=RT \) equation is:

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

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

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

The translational degrees of freedom \( (f_t) \) and rotational degrees of freedom \( (f_r) \) of \( CH_4 \) molecule are:

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

A thermodynamic system is taken from an original state A to an intermediate state B by a linear process as shown in the figure. It’s 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:

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

\( N \) 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:

The pressure and volume of an ideal gas are related as \( PV^{3/2} = K \) (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:

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

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

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

Two vessels \( A \) and \( B \) are of the same size and are at same temperature. \( A \) contains \( 1 \, \text{g} \) of hydrogen and \( B \) contains \( 1 \, \text{g} \) of oxygen. \( P_A \) and \( P_B \) are the pressure of the gases in \( A \) and \( B \) respectively, then \( \frac{P_A}{P_B} \) is:

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

The average kinetic energy of a monoatomic molecule is \( 0.414 \, \text{eV} \) at temperature: (Use \( K_B = 1.38 \times 10^{-23} \, \text{J} / \text{mol} - \text{K} \) )

If the root mean square velocity of hydrogen molecule at a given temperature and pressure is \( 2 \, \text{km/s} \), the root mean square velocity of oxygen at the same condition in km/s is:

Two thermodynamical processes 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.

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

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 \( n \) is the number: density and \( d \) 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:

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JEE Main 2024 8th April Morning Shift

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