Five moles of hydrogen initially at $STP$ is compressed adiabatically so that its temperature becomes $673 \, K$. The increase in internal energy of the gas, in kilo joule is $(R=8.3 \, J/mol-K; \gamma=1.4$ for diatomic gas$)$

$A$ diatomic gas $\left(\gamma = \frac{7}{5}\right)$ is compressed adiabatically to volume $\frac{V_0}{32}$,where $V_0$ is its initial volume. The initial temperature of the gas is $T_i$ in Kelvin and the final temperature is $xT_i$ in Kelvin. The value of $x$ is:

We consider a thermodynamic system. If $\Delta U$ represents the increase in its internal energy and $W$ the work done by the system,which of the following statements is true?

$A$ gas is compressed adiabatically until its temperature is doubled. The ratio of its final volume to initial volume will be

An ideal gas in a cylinder is compressed adiabatically to one-third of its original volume. $A$ work of $45 \,J$ is done on the gas by the process. The change in internal energy of the gas and the heat flowed into the gas,respectively are

One mole of nitrogen gas being initially at a temperature of $T_0 = 300 \,K$ is adiabatically compressed to increase its pressure $10$ times. The final gas temperature after compression is (Assume,nitrogen gas molecules as rigid diatomic and $100^{1/7} = 1.9$) (in $\,K$)