$A$ gas system is taken through the thermodynamic cyclic process $1 \rightarrow 2 \rightarrow 3 \rightarrow 1$ as shown in the figure. The amount of heat released by the system is

In a thermodynamic process,the pressures and volumes corresponding to some points in the figure are $P_A = 3 \times 10^4 \, Pa$,$V_A = 2 \times 10^{-3} \, m^3$,$P_B = 8 \times 10^4 \, Pa$,and $V_D = 5 \times 10^{-3} \, m^3$. In process $AB$,$600 \, J$ of heat is added,and in process $BC$,$200 \, J$ of heat is added to the system. The change in the internal energy in process $AC$ would be .... $J$.

An ideal system can be brought from state $A$ to $B$ through four paths as shown in the figure. The energy given to the system is minimum in

In the given figure,two processes $A$ and $B$ are shown by which a thermodynamic system goes from an initial state $i$ to a final state $f$. If $\Delta Q_A$ and $\Delta Q_B$ are respectively the heats supplied to the systems,then:

In the following figures $(a)$ to $(d)$,the variation of volume with change of pressure is shown. The gas is taken along the path $A B C D A$. The change in internal energy of the gas will be .......

The pressure of a gas changes linearly with volume from $A$ to $B$ as shown in the figure. If no heat is supplied to or extracted from the gas,then the change in the internal energy of the gas will be $............\,J$.