An ideal gas having initial pressure $P$, volume $V$ and temperature $T$ is allowed to expand adiabatically until its volume becomes $4V$, while its temperature falls to $T/2$. If the work done by the gas during the expansion is $\alpha PV$, the value of $\alpha$ is

What is the name of the ideal-gas process in which no heat is transferred?

An ideal gas at pressure $p$ is adiabatically compressed so that its density becomes twice that of the initial. If $\gamma = \frac{c_p}{c_v} = \frac{7}{5}$,then the final pressure of the gas is:

Which of the following is true in the case of an adiabatic process, where $\gamma = C_p / C_V$?

$A$ monoatomic ideal gas,initially at temperature $T_1$,is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature $T_2$ by releasing the piston suddenly. If $L_1$ and $L_2$ are the lengths of the gas column before and after expansion respectively,then $T_1/T_2$ is given by

Consider a thermodynamic process where internal energy $U = A P^2 V$ $(A = \text{constant})$. If the process is performed adiabatically, then: