Which of the following curves represent the variation of coefficient of volume expansion of an ideal gas at constant pressure?

A number of Carnot engines are operated at identical cold reservoir temperatures $$(T_L)$$. However, their hot reservoir temperatures are kept different. A graph of the efficiency of the engines versus hot reservoir temperature $$(T_H)$$ is plotted. The correct graphical representation is

A gas mixture contains monoatomic and diatomic molecules of 2 moles each. The mixture has a total internal energy of (symbols have usual meanings)

A sphere, a cube and a thin circular plate all of same material and same mass initially heated to same high temperature are allowed to cool down under similar conditions. Then, the