A cyclic process $ABCD$ is shown in the figure $P-V$ diagram. Which of the following curves represent the same process

A closed container contains a homogeneous mixture of two moles of an ideal monatomic gas $(\gamma=5 / 3)$ and one mole of an ideal diatomic gas $(\gamma=7 / 5)$. Here, $\gamma$ is the ratio of the specific heats at constant pressure and constant volume of an ideal gas. The gas mixture does a work of $66$ Joule when heated at constant pressure. The change in its internal energy is. . . . . . .Joule.

Consider $1 \,kg$ of liquid water undergoing change in phase to water vapour at $100^{\circ} C$. At $100^{\circ} C$, the vapour pressure is $1.01 \times 10^5 \,N – m ^2$ and the latent heat of vaporization is $22.6 \times 10^5 \,Jkg ^{-1}$. The density of liquid water is $10^3 \,kg m ^{-3}$ and that of vapour is $\frac{1}{1.8} \,kg m ^{-3}$. The change in internal energy in this phase change is nearly ………… $\,J kg ^{-1}$

An ideal monoatomic gas is taken through the thermodynamic states $A \to B \to C \to D$ via the paths shown in the figure. If $U_A, U_B, U_C$ and $U_D$ represent the internal energy of the gas in state $A, B\, C$ and $D$ respectively, then which of the following is not true?

If $Q , E$ and $W$ denote respectively the heat added, change in internal energy and the work done by a closed cycle process, then