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 :

A 15 g mass of nitrogen gas is enclosed in a vessel at a temperature 27^oC. Amount of heat transferred to the gas, so that rms velocity of molecules is doubled, is about : [Take R = 8.3 J/K mole]

A mixture of 2 moles of helium gas (atomic mass = 4 u), and 1 mole of argon gas (atomic mass = 40 u) is kept at 300 K in a container. The ratio of their rms speeds $$\left[ {{{{V_{rms}}\,(helium)} \over {{V_{rms}}\,(\arg on)}}} \right],$$ is close to :

Temperature difference of 120^oC is maintained between ends of a uniform rod AB of length 2L. Another bent rod PQ, of same cross-section as AB and length $${{3L} \over 2},$$ is connected across AB (see figure). In steady state, temperature difference between P and Q will be close to :