JEE Main Heat and Thermodynamics Practice Questions With Solutions

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

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

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

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

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

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 $({27}^{\circ }\mathrm{C})$\left(\right. 27^{\circ} C \left.\right). The ratio of specific heat of gases at constant volume respectively is:

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

Given below are two statements:

Statement (I) : Dimensions of specific heat is $[{\mathrm{L}}^2{\mathrm{T}}^{-2}{\mathrm{K}}^{-1}]$\left[\right. L^{2} \left(\textrm{ } T\right)^{- 2} \left(\textrm{ } K\right)^{- 1} \left]\right..

Statement (II) : Dimensions of gas constant is $[\mathrm{M}{\mathrm{L}}^2{\mathrm{T}}^{-1}{\mathrm{K}}^{-1}]$\left[\right. M L^{2} \left(\textrm{ } T\right)^{- 1} \left(\textrm{ } K\right)^{- 1} \left]\right..

In the light of the above statements, choose the most appropriate answer from the options given below.

Energy of 10 non rigid diatomic molecules at temperature $\mathrm{T}$T is :