One mole of an ideal gas is taken through an adiabatic process where the temperature rises from 27$$^\circ$$ C to 37$$^\circ$$ C. If the ideal gas is composed of polyatomic molecule that has 4 vibrational modes, which of the following is true? [R = 8.314 J mol^$$-$$1 k^$$-$$1]

Two Carnot engines A and B operate in series such that engine A absorbs heat at T₁ and rejects heat to a sink at temperature T. Engine B absorbs half of the heat rejected by Engine A and rejects heat to the sink at T₃. When workdone in both the cases is equal, to value of T is :

The number of molecules in one litre of an ideal gas at 300 K and 2 atmospheric pressure with mean kinetic energy 2 $$\times$$ 10^$$-$$9 J per molecules is :

In the reported figure, there is a cyclic process ABCDA on a sample of 1 mol of a diatomic gas. The temperature of the gas during the process A $$\to$$ B and C $$\to$$ D are T₁ and T₂ (T₁ > T₂) respectively.


Choose the correct option out of the following for work done if processes BC and DA are adiabatic.