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).

There are two samples $A$ and $B$ of a certain gas,which are initially at the same temperature and pressure. Both are compressed from volume $V$ to $\frac{V}{2}$. Sample $A$ is compressed isothermally while sample $B$ is compressed adiabatically. The final pressure of $A$ is

$2$ moles of an ideal monoatomic gas is carried from a state $(p_{0}, V_{0})$ to state $(2 p_{0}, 2 V_{0})$ along a straight line path in a $p-V$ diagram. The amount of heat absorbed by the gas in the process is given by

The pressure $p$,volume $V$ and temperature $T$ for a certain gas are related by $p=\frac{A T-B T^{2}}{V}$ where $A$ and $B$ are constants. The work done by the gas when the temperature changes from $T_{1}$ to $T_{2}$ while the pressure remains constant,is given by

Initial pressure and volume of a gas are $P$ and $V$ respectively. First,its volume is expanded to $4V$ by an isothermal process,and then its volume is reduced to $V$ by an adiabatic process. Find its final pressure if $\gamma = \frac{3}{2}$.

Check if the following statements are true or false:
$1.$ For an adiabatic process,$T V^{\gamma - 1} = \text{constant}$.
$2.$ The charging process of a battery is a reversible process.
$3.$ Water falling from a height is a reversible process.
$4.$ Internal energy,volume,and mass are intensive variables,while pressure,temperature,and density are extensive variables.