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

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

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

The amount of heat energy required to raise the temperature of 1 g of Helium at NTP, from T₁K to T₂K is