The total internal energy change for a reversible isothermal cycle is

For $1 \, \text{mole}$ of an ideal gas,isothermal expansion occurs from a volume of $2 \, L$ to $6 \, L$ at a temperature of $300 \, K$. The value of $\Delta U$ for this process is .............

Match List-$I$ with List-$II$.

List-$I$ (Process)	List-$II$ (Conditions)
$A$. Isothermal process	$I$. No heat exchange
$B$. Isochoric process	$II$. Carried out at constant temperature
$C$. Isobaric process	$III$. Carried out at constant volume
$D$. Adiabatic process	$IV$. Carried out at constant pressure

Choose the correct answer from the options given below:

Among the following,the number of state variables is $.....$
Internal energy $(U)$; Volume $(V)$; Heat $(q)$; Enthalpy $(H)$

Find the work done on $2 \ mol$ of an ideal gas at $27^{\circ} C$ if it is compressed reversibly and isothermally from $5.05 \times 10^6 \ Nm^{-2}$ to $1.01 \times 10^5 \ Nm^{-2}$ pressure. (in $kJ$)

Two moles of an ideal gas are compressed isothermally and reversibly from $40 \ L$ to $20 \ L$ at $300 \ K$. What is the work done (in $kJ$)? $(R=8.314 \ J \ K^{-1} \ mol^{-1})$