An ideal gas undergoes an adiabatic process obeying the relation $PV^{4/3} = \text{constant}$. If its initial temperature is $300 \ K$ and its pressure is increased up to four times its initial value, then the final temperature is (in Kelvin):

The work done in an adiabatic change in an ideal gas depends upon only

$A$ monatomic gas at a pressure of $100 \text{ kPa}$ expands adiabatically such that its final volume becomes $8$ times its initial volume. If the work done during the process is $180 \text{ J}$, then the initial volume of the gas is (in $\text{ cm}^3$)

Which of the following statements is true? ($\Delta U = \text{increase in internal energy}$,$dW = \text{work done by the system}$)

$A$ reversible adiabatic path on a $P-V$ diagram for an ideal gas passes through state $A$ where $P = 0.7 \times 10^5 \, N/m^2$ and $V = 0.0049 \, m^3$. The ratio of specific heats of the gas is $1.4$. The slope of the path at $A$ is:

$A$ diesel engine has a compression ratio of $20:1$. If the initial pressure is $1 \times 10^5 \ Pa$ and the initial volume of the cylinder is $1 \times 10^{-3} \ m^3$, then how much work does the gas do during the compression (in $J$)? (Assume the process as adiabatic) $(C_V=20.8 \ J/mol \ K, \gamma=1.4, (20)^{1.4}=66.3)$