During an adiabatic compression, $830\, J$ of work is done on $2\, moles$ of a diatomic ideal gas to reduce its volume by $50\%$. The change in its temperahture is nearly….. $K$ $(R\, = 8.3\, J\,K^{-1}\, mol^{-1} )$

The variation of pressure $P$ with volume $V$ for an ideal monatomic gas during an adiabatic process is shown in figure. At point $A$ the magnitude of rate of change of pressure with volume is

Following figure shows on adiabatic cylindrical container of volume ${V_0}$ divided by an adiabatic smooth piston (area of cross-section = $A$ ) in two equal parts. An ideal gas $({C_P}/{C_V} = \gamma )$ is at pressure $P_1$ and temperature $T_1$ in left part and gas at pressure $P_2$ and temperature $T_2$ in 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)

The volume of air increases by $5\%$ in its adiabatic expansion. The percentage decrease in its pressure will be …… $\%$

Two identical samples of a gas are allowed to expand $(i)$ isothermally $(ii)$ adiabatically. Work done is