The mean free path of molecules of a gas, (radius r) is inversely proportional to

In a vessel, the gas is at pressure P. If the mass of all the molecules is halved and their speed is doubled, then the resultant pressure will be

Two Carnot engines A and B are operated in series. The engine A receives heat from the source at temperature T₁ and rejects the heat to the sink at temperature T. The second engine B receives the heat at temperature T and rejects to its sink at temperature T₂. For what values of T the efficiencies of the two engines are equal

A system is taken from state a to state c by two paths adc and abc as shown in the figure. The internal energy at a is $${U_a} = 10\,J$$. Along the path adc the amount of heat absorbed dQ₁ $$=$$ 50 J and the work obtained dW₁ $$=$$ 20 J whereas along the path abc the heat absorbed dQ₂ = 36 J. The amount of work allong the path abc is