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A certain gas is isothermally compressed to \( \left( \frac{1}{3} \right)^{\text{rd}} \) of its initial volume \( (V_0 = 3\,\text{litre}) \) by applying required pressure. If the bulk modulus of the gas is \( 3 \times 10^{5}\ \mathrm{N/m^{2}} \), the magnitude of work done on the gas is ______ \( \text{J} \).

An ideal gas undergoes a process maintaining relation between pressure \( (P) \) and Volume \( (V) \) as \( P=P_0\left(1+\left(\dfrac{V_0}{V}\right)^2\right)^{-1} \), where \( P_0 \) and \( V_0 \) are constants. If two samples \( A \) and \( B \) (two moles each) with initial volumes \( V_0 \) and \( 3V_0 \) respectively undergo above mentioned process and attain same pressure, then the difference at the temperatures of these samples, \( T_B-T_A \) is _______.
\( (R=\text{gas constant}) \)

When \( 300 \, \text{J} \) of heat given to an ideal gas with \( C_{p} = \dfrac{7}{2} R \) its temperature raises from \( 20^\circ \text{C} \) to \( 50^\circ \text{C} \) keeping its volume constant. The mass of the gas is (approximately) __________ \( \text{g} \). \( ( R = 8.314/\text{mol.K} ) \).

\( 10 \) mole of oxygen is heated at constant volume from \( 30^\circ\text{C} \) to \( 40^\circ\text{C} \). The change in the internal energy of the gas is __________ \( \text{cal} \). (The molecular specific heat of oxygen at constant pressure, \( C_p = 7 \, \text{cal} / \text{mol}^\circ\text{C} \) and \( R = 2 \, \text{cal}./\text{mol}.^\circ\text{C} \))

Heat is supplied to a diatomic gas at constant pressure. Then the ratio of \( \Delta Q : \Delta U : \Delta W \) is ______.

A cylindrical tube \( AB \) of length \( l \), closed at both ends contains an ideal gas of \( 1 \, \text{mol} \) having molecular weight \( M \). The tube is rotated in a horizontal plane with constant angular velocity \( \omega \) about an axis perpendicular to \( AB \) and passing through the edge at end \( A \), as shown in the figure. If \( P_{A} \) and \( P_{B} \) are the pressures at \( A \) and \( B \) respectively, then: (Consider the temperature is same at all points in the tube)

The internal energy of a monoatomic gas is \( 3nRT \). One mole of helium is kept in a cylinder having internal cross section area of \( 17\,\text{cm}^{2} \) and fitted with a light movable frictionless piston. The gas is heated slowly by supplying \( 126\,\text{J} \) heat. If the temperature rises by \( 4^{\circ}\text{C} \), then the piston will move ______ cm.
\( \text{(atmospheric pressure } = 10^{5}\ \text{Pa)} \)

In the following \( p\! -\! V \) diagram the equation of state along the curved path is given by \( (V - 2)^{2} = 4 a p \) where \( a \) is a constant. The total work done in the closed path is:

A cylinder with adiabatic walls is closed at both ends and is divided into two compartments by a frictionless adiabatic piston. Ideal gas is filled in both (left and right) the compartments at same \( P \), \( V \), \( T \). Heating is started from left side until pressure changes to \( 27\dfrac{P}{8} \). If initial volume of each compartment was \( 9 \) litres then the final volume in right-hand side compartment is ______ litres. (for this ideal gas \( C_{p}/C_{r}=1.5 \))

Density of water at \( 4^\circ \text{C} \) and \( 20^\circ \text{C} \) are \( 1000 \, \text{kg/m}^3 \) and \( 998 \, \text{kg/m}^3 \) respectively. The increase in internal energy of \( 4 \, \text{kg} \) of water when it is heated from \( 4^\circ \text{C} \) to \( 20^\circ \text{C} \) is _____ \( \text{J} \).
(Specific heat capacity of water \( = 4.2 \, \text{J/kg} \) and \( 1 \) atmospheric pressure \( = 10^5 \, \text{Pa} \))

Initial pressure and volume of a monoatomic ideal gas are \( P \) and \( V \). The change in internal energy of this gas in adiabatic expansion to volume \( V_{\text{final}} = 27V \) is ______ \( \text{J} \).

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: If the average kinetic energy of \( \mathrm{H_2} \) and \( \mathrm{O_2} \) molecules, kept in two different sized containers are same, then their temperatures will be same.
Reason R: The r.m.s. speed of \( \mathrm{H_2} \) and \( \mathrm{O_2} \) molecules are same at same temperature.
Choose the correct answer from the options given below:

An insulated cylinder of volume \( 60 \, \text{cm}^{3} \) is filled with a gas at \( 27^\circ \text{C} \) and \( 2 \) atmospheric pressure. Then the gas is compressed making the final volume as \( 20 \, \text{cm}^{3} \) while allowing the temperature to rise to \( 77^\circ \text{C} \). The final pressure is ______ atmospheric pressure.

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Statement I: Change in internal energy of a system containing \( n \) mole of ideal gas can be written as \( \Delta U = nC_v (T_f - T_i) - \frac{nR}{\gamma - 1} (T_f - T_i) \), where \( \gamma = \frac{C_p}{C_v} \), \( T_i \) = initial temperature, \( T_f \) = final temperature.
Statement II: Relation between degree of freedom \( f \) and \( \gamma(= \frac{C_p}{C_v}) \) is \( \left( \gamma = 1 + \frac{2}{f} \right) \).
Choose the correct answer from the options given below

\( 10 \) mole of an ideal gas is undergoing the process shown in the figure. The heat involved in the process from \( P_1 \) to \( P_2 \) is \( a \) Joule \( ( P_1 = 21.7 \, \text{Pa} \text{ and } P_2 = 30 \, \text{Pa}, \, C_v = 21 \, \text{J} / \text{K} \cdot \text{mol} \, R = 8.3 \, \text{J} / \text{molK} ) \). The value of \( a \) is ________ .

If \( 2 \) mole of an ideal monoatomic gas at temperature \( T \), is mixed with \( 6 \) mole of another ideal monoatomic gas at temperature \( 2T \) then the temperature of mixture is:

Consider the following statements:
A. Zeroth law of thermodynamics gives concept of temperature
B. First law of thermodynamics gives concept of internal energy
C. In isothermal expansion of ideal gas, \( \Delta Q \neq \Delta W \)
D. Product of intensive and extensive variables is extensive
E. The ratio of any extensive variable to mass will be an extensive variable

A mixture of carbon dioxide and oxygen has volume \( 8310 \, \text{cm}^{3} \), temperature \( 300 \, \text{K} \), pressure \( 100 \, \text{kPa} \) and mass \( 13.2 \, \text{g} \). The number of moles of carbon dioxide and oxygen gases in the mixture respectively are ________.
(Assume both carbon dioxide and oxygen gases behave like ideal gases) \([ R = 8.31 \, \text{J}/(\text{mol}\cdot\text{K}) ]\)

One mole of diatomic gas having rotational modes only is kept in a cylinder with a piston system. The cross-section area of the cylinder is \( 4 \, \text{cm}^2 \). The gas is heated slowly to raise the temperature by \( 1.2^\circ \text{C} \) during which the piston moves by \( 25 \, \text{mm} \). The amount of heat supplied to the gas is ______ \( \text{J} \). (Neglect mass of the piston) [Atmospheric pressure = \( 100 \, \text{kPa} \), \( R = 8.3 \, \text{J} \, \text{mol}^{-1} \, \text{K}^{-1} \)]

A diatomic gas \( (\gamma = 1.4) \) does \( 100 \; \text{J} \) of work when it is expanded isobarically. Then the heat given to the gas __________ \( \text{J} \).

One gas of \( n_1 \) mole of molecules at temperature \( T_1 \), volume \( V_1 \), and pressure \( P_1 \) and another gas of \( n_2 \) mole of molecules at temperature \( T_2 \), volume \( V_2 \) and pressure \( P_2 \), are mixed resulting in pressure \( P \) and volume \( V \) of the mixture. The temperature of the mixture is _______.

An air bubble of volume \( 2.9 \, \text{cm}^3 \) rises from the bottom of a swimming pool of \( 5 \, \text{m} \) deep. At the bottom of the pool water temperature is \( 17^\circ\text{C} \). The volume of the bubble when it reaches the surface, where the water temperature is \( 27^\circ\text{C} \), is ______ \( \text{cm}^3 \).
\( (g = 10 \, \text{m/s}^2 , \ \text{density of water} = 10^3 \, \text{kg/m}^3 , \text{ and } 1 \, \text{atm pressure is } 10^5 \, \text{Pa}) \)

The r.m.s. speed of oxygen molecules at \( 47^\circ \text{C} \) is equal to that of the hydrogen molecules kept at _______ \( ^\circ \text{C} \). (Mass of oxygen molecule/mass of hydrogen molecule = \( 32/2 \))

Two closed vessels of same volume are joined through a narrow tube and both vessels are filled with air of pressure \( 90 \, \text{kPa} \) and temperature \( 400 \, \text{K} \). Keeping the temperature of one vessel constant at \( 400 \, \text{K} \) the second vessel temperature is raised to \( 500 \, \text{K} \). The final pressure in the vessels is _____ \( \text{kPa} \).

A gas of certain mass filled in a closed cylinder at a pressure of \( 3.23 \, \text{kPa} \) has temperature \( 50^\circ \text{C} \). The gas is now heated to double its temperature. The modified Pressure is ______ \( \text{Pa} \).

\( 5 \) moles of unknown gas is heated at constant volume from \( 10^{\circ}\text{C} \) to \( 20^{\circ}\text{C} \). The molar specific heat of this gas at constant pressure \( C_{p}=8\ \text{cal}/\text{mol}\cdot{}^{\circ}\text{C} \) and \( R=8.36\ \text{J}/\text{mol}\cdot{}^{\circ}\text{C} \). The change in the internal energy of the gas is ______ calorie.

The volume of an ideal gas increases \( 8 \) times and temperature becomes \(( \frac{1}{4} \))th of initial temperature during a reversible change. If there is no exchange of heat in this process \( (\Delta Q = 0) \) then identify the gas from the following options (Assuming the gases given in the options are ideal gases):

Consider two boxes containing ideal gases \( A \) and \( B \) such that their temperatures, pressures and number densities are same. The molecular size of \( A \) is half of that of \( B \) and mass of molecule \( A \) is four times that of \( B \). If the collision frequency in gas \( B \) is \( 32 \times 10^{18} / \text{s} \) then collision frequency in gas \( A \) is ________ \( / \text{s} \).

A vessel contains \( 0.15 \, \text{m}^3 \) of a gas at pressure \( 8 \) bar and temperature \( 140^\circ \text{C} \) with \( c_p = 3R \) and \( c_v = 2R \). It is expanded adiabatically till pressure falls to \( 1 \) bar. The work done during this process is ______ \( \text{kJ} \). (\( R \) is gas constant)

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JEE Main 2026 6th April Evening Shift

If \( 2 \) mole of an ideal monoatomic gas at temperature \( T \), is mixed with \( 6 \) mole of another ideal monoatomic gas at temperature \( 2T \) then the temperature of mixture is: