A Container having $1\ mole$ of a gas at a temperature $27\ ^oC$ has a movable piston which maintains at constant pressure in container of $1\ atm.$ The gas is compressed until temperature becomes $127^oC.$ The work done is …….. $J$ $(C_p\ for\  gas\  is\  7.03\ cal/mol-K)$

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

The figure shows the $P-V$ plot of an ideal gas taken through a cycle $ABCDA$. The part $ABC$ is a semi-circle and $CDA$ is half of an ellipse. Then,

$(A)$ the process during the path $\mathrm{A} \rightarrow \mathrm{B}$ is isothermal

$(B)$ heat flows out of the gas during the path $\mathrm{B} \rightarrow \mathrm{C} \rightarrow \mathrm{D}$

$(C)$ work done during the path $\mathrm{A} \rightarrow \mathrm{B} \rightarrow \mathrm{C}$ is zero

$(D)$ positive work is done by the gas in the cycle $ABCDA$

A thermodynamic process is shown in the figure. The pressures and volumes corresponding to some points in the figure are :

${P_A} = 3 \times {10^4}Pa,\;{P_B} = 8 \times {10^4}Pa$ and ${V_A} = 2 \times {10^{ – 3}}{m^3},\;{V_D} = 5 \times {10^{ – 3}}{m^3}$

In process $AB$, $600 J$ of heat is added to the system and in process $BC, 200 J $ of heat is added to the system. The change in internal energy of the system in process $ AC$ would be …… $J$

$P-V$ diagram of a cyclic process $ABCA$ is as shown in figure. Choose the correct statement