An ideal gas expands adiabatically, $(\gamma = 1.5)$. To reduce the root-mean-square (r.m.s.) velocity of the molecules $4$ times, the gas has to be expanded by a factor of: (in $times$)

For an adiabatic process,the pressure and temperature of a monoatomic gas are related as $P \propto T^{c}$. Then,$c = $.......

When air of the atmosphere rises up,it cools. Why?

In an adiabatic process,which of the following statements is true?

$A$ triatomic gas at an initial temperature of $18^{\circ}C$ is compressed adiabatically to $1/8$ of its initial volume. What is the final temperature of the gas?

The following figure shows an adiabatic cylindrical container of volume $V_0$ divided by an adiabatic smooth piston (area of cross-section = $A$) into two equal parts. An ideal gas $(C_P/C_V = \gamma)$ is at pressure $P_1$ and temperature $T_1$ in the left part,and a gas at pressure $P_2$ and temperature $T_2$ is in the right part. The piston is slowly displaced and released at a position where it can stay in equilibrium. The final pressure of the two parts will be (Suppose $x$ = displacement of the piston):