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)

An insulated container of gas has two chambers separated by an insulating partition. One of the chambers has volume $${V_1}$$ and contains ideal gas at pressure $${P_1}$$ and temperature $${T_1}$$. The other chamber has volume $${V_2}$$ and contains ideal gas at pressure $${P_2}$$ and temperature $${T_2}$$. If the partition is removed without doing any work on the gas, the final equilibrium temperature of the gas in the container will be

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