An unknown metal of mass 192 g heated to a temperature of 100^oC was immersed into a brass calorimeter of mass 128 g containing 240 g of water at a temperature of 8.4^oC. Calculate the specific heat of the unknown metal if water temperature stabilizes at 21.5^oC. (Specific heat of brass is 394 J kg^–1 K^–1)

A heat source at T = 10³ K is connected to another heat reservoir at T = 10² K by a copper slab which is 1 mthick. Given that the thermal conductivity of copper is 0.1 WK^–1m^–1, the energy flux through it in the steady state is -

Three Carnot engines operate in series between a heat source at a temperature T₁ and a heat sink at temperature T₄ (see figure). There are two other reservoirs at temperature T₂ and T₃, as shown, with T₁ > T₂ > T₃ > T₄. The three engines are equally efficient if -

Two Carnot engines A and B are operated in series. The first one, A, receives heat at T₁ (= 600 K) and rejects to a reservoir at temperature T₂. The second engine B receives heat rejected by the first engine and, in tum, rejects to a heat reservoir at T₃ (=400 K). Calculate the temperature T₂ if the work outputs of the two engines are equal :