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

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

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 $\left(\gamma=1+\frac{2}{f}\right)$

Choose the correct answer from the options given below