Match the List-$I$ with List-$II$:

List-$I$	List-$II$
$A$. Pressure varies inversely with volume of an ideal gas.	$I$. Adiabatic process
$B$. Heat absorbed goes partly to increase internal energy and partly to do work.	$II$. Isochoric process
$C$. Heat is neither absorbed nor released by a system.	$III$. Isothermal process
$D$. No work is done on or by a gas.	$IV$. Isobaric process

An insulating cylinder contains $4 \text{ moles}$ of an ideal diatomic gas. When a heat $Q$ is supplied to it, $2 \text{ moles}$ of the gas molecules dissociate. If the temperature of the gas remains constant, then the value of $Q$ is ($R$ - universal gas constant).

The molar heat capacity in a process of a diatomic gas,if it does a work of $\frac{Q}{4}$ when a heat of $Q$ is supplied to it,is

In thermodynamics,heat and work are

Neon gas of a given mass expands isothermally to double its volume. What should be the further fractional decrease in pressure,so that the gas when adiabatically compressed from that state,reaches the original state?

$A$ thermodynamic system is taken from an initial state $i$ with internal energy $U_i = 100 \ J$ to the final state $f$ along two different paths $iaf$ and $ibf$,as schematically shown in the figure. The work done by the system along the paths $ia$,$af$,$ib$ and $bf$ are $W_{ia} = 50 \ J$,$W_{af} = 200 \ J$,$W_{ib} = 50 \ J$ and $W_{bf} = 100 \ J$ respectively. The heat supplied to the system along the paths $iaf$ and $ibf$ are $Q_{iaf}$ and $Q_{ibf}$ respectively. If the internal energy of the system in the state $b$ is $U_b = 200 \ J$ and $Q_{iaf} = 500 \ J$,the ratio $Q_{ibf} / Q_{iaf}$ is: