The adjoining figure show the $P-V$ plot of an ideal gas taken through a cycle $ABCDA.$ The part $\mathrm{ABC}$ is a semi-circle and $\mathrm{CDA}$ is half of an ellipse. Then select the correct statement$\left(\mathrm{s}\right)$ from the following :

                                                                                                                                                         

$100 \mathrm{g}$ of water is heated from $30°\mathrm{C}$ to$50°\mathrm{C}$. Ignoring the slight expansion of the water, the change in its internal energy is $($specific heat of water is $4184 \mathrm{J} {\mathrm{kg}}^{-1} {\mathrm{K}}^{-1})$.

A thermally insulated vessel contains an ideal gas of molecular mass $M$ and a ratio of specific heats $\gamma$. It is moving with speed $v$ and is suddenly brought to rest. Assuming no heat is lost to the surroundings, its temperature increases by,

Helium gas goes through a cycle $ABCDA$ $($consisting of two isochoric and two isobaric lines$)$ as shown in the figure. Efficiency of this cycle is nearly : $($Assume the gas to be close to ideal gas$)$

In a process carried on an ideal gas, $\mathrm{W}=0 \mathrm{and} \mathrm{Q}<0.$ Then, of the gas:

One mole of diatomic ideal gas undergoes a cyclic process $\mathrm{ABC}$ as shown in figure. The process $\mathrm{BC}$ is adiabatic. The temperature at $\mathrm{A}$, $\mathrm{B}$ and $\mathrm{C}$ are $400 \mathrm{K}$, $800 \mathrm{K}$ and $600 \mathrm{K}$ respectively. Choose the correct statement.

If $\mathrm{Q}, ∆\mathrm{U} \mathrm{and} \mathrm{W}$ denote respectively the heat added, change in internal energy and the work done in a closed cycle process, then:

A system goes from the state $A$ to the state $B$ via two process $1 \mathrm{and} 2$ as shown figure. If $∆{\mathrm{U}}_1 \mathrm{and} ∆{\mathrm{U}}_2$ are the changes in internal energies in the process $1 \mathrm{and} 2$ respectively, then

An ideal is filled in a closed, rigid and thermally-insulated container. A coil of $100\mathrm{\Omega }$ resistance and carrying a current of $1 \mathrm{A}$ supplies heaT to the gas. The change in the internal energy of the gas after $5$ minutes will be: