The speed of sound in oxygen $$\left( {{O_2}} \right)$$ at a certain temperature is $$460\,\,m{s^{ - 1}}.$$ The speed of sound in helium $$(He)$$ at the same temperature will be (assume both gases to be ideal)

When a system is taken from state $$i$$ to state $$f$$ along the path iaf, it is found that $$Q=50$$ cal and $$W=20$$ $$cal$$. Along the path $$ibf$$ $$Q=36$$ $$cal.$$ $$W$$ along the path $$ibf$$ is

A Carnot engine, having an efficiency of $$\eta = 1/10$$ as heat engine, is used as a refrigerator . If the work done on the system is $$10$$ $$J$$, the amount of energy absorbed from the reservoir at lower temperature is

If $${C_p}$$ and $${C_v}$$ denote the specific heats of nitrogen per unit mass at constant pressure and constant volume respectively, then