An ideal gas at pressure $P$ and temperature $T$ is expanding such that $P T^3=$ constant. The coefficient of volume expansion of the gas is $\_\_\_\_$ .

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason $\mathbf{R}$

Statement I : Change in internal energy of a system containing $n$ mole of ideal gas can be written as $\Delta \mathrm{U}=n \mathrm{C}_v\left(T_{\mathrm{f}}-T_i\right)=\frac{n R}{\gamma-1}\left(T_{\mathrm{f}}-T_i\right)$, where $\gamma=\frac{C_p}{C_v}, T_i=$ initial temperature, $T_{\mathrm{f}}=$ final temperature.

Statement II : Relation between degree of freedom $f$ and $\gamma\left(=C_p / C_v\right)$ is $\left(\gamma=1+\frac{2}{f}\right)$

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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

Choose the correct combination of statements from the options given below:

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.

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