One mole of an ideal monoatomic gas is heated at a constant pressure of one atmosphere from $0^{\circ}C$ to $100^{\circ}C$. Then the change in the internal energy is

For the given $P-V$ diagram of a thermodynamic system,match the curves with their respective thermodynamic processes. ($P$ = Pressure and $V$ = Volume)

Curve	Process
$I$	$a)$ Adiabatic
$II$	$b)$ Isobaric
$III$	$c)$ Isochoric
$IV$	$d)$ Isothermal

One mole of an ideal gas undergoes a cyclic process,consisting of two isochores and two isobars. Temperatures at points $1$ and $3$ are $T_1$ and $T_3$ respectively. Find the work done by the gas over the cycle,if points $2$ and $4$ lie on the same isotherm.

Three processes compose a thermodynamic cycle shown in the $PV$ diagram. Process $1\rightarrow 2$ takes place at constant temperature. Process $2\rightarrow 3$ takes place at constant volume,and process $3\rightarrow 1$ is adiabatic. During the complete cycle,the total amount of work done is $10\,J$. During process $2\rightarrow 3$,the internal energy decreases by $20\,J$ and during process $3\rightarrow 1$,$20\,J$ of work is done on the system. How much heat is added to the system during process $1\rightarrow 2$ (in $,J$)?

An ideal gas is taken reversibly around the cycle $a-b-c-d-a$ as shown on the temperature $T$ - entropy $S$ diagram. The most appropriate representation of the above cycle on an internal energy $U$ - volume $V$ diagram is

The efficiency of a heat engine is $\eta$ and the coefficient of performance of a refrigerator is $\beta$. Then: