Figure shows a cylindrical adiabatic container of total volume $2V_0$ divided into two equal parts by a conducting piston (which is free to move). Each part containing identical gas at pressure $P_0$ . Initially temperature of left and right part is $4T_0$ and $T_0$ respectively. An external force is applied on the piston to keep the piston at rest. Find the value of external force required when thermal equilibrium is reached. ( $A =$ Area of piston)
$\frac{8}{5}{P_0}A$
$\frac{2}{5}{P_0}A$
$\frac{5}{6}{P_0}A$
$\frac{6}{5}{P_0}A$
$Assertion :$ Adiabatic expansion is always accompanied by fall in temperature.
$Reason :$ In adiabatic process, volume is inversely proportional to temperature.
The work of $146\,kJ$ is performed in order to compress one kilo mole of a gas adiabatically and in this process the temperature of the gas increases by $7\,^oC$ . The gas is $(R = 8.3\, J\, mol^{-1}\, K^{-1})$
Initial pressure and volume of a gas are $P$ and $V$ respectively. First it is expanded isothermally to volume $4V$ and then compressed adiabatically to volume $V$ . The final pressure of gas will be (given $\gamma = 3/2$ )
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