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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 4th April Morning Shift

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: