Q4. 3 mol of helium in a rigid container is heated from 300 K to 320 K. How much heat does it take?
Q = μCvΔT, where μ = 3 is the number of moles: 3 × (3/2) × 8.31 × 20, about 748 J.
Q5. Carbon dioxide is a linear molecule. Treating it as rigid, predict its Cv.
A linear molecule has 3 translational and 2 rotational degrees of freedom, like a diatomic one, so Cv = (5/2)R, about 20.8 J mol K. (Its measured value is higher, because some vibrations are excited.) This is beyond NCERT: NCERT Table 12.1 gives 3R for triatomic gases, which holds for non-linear ones.
Q6. Why does kinetic theory give C = 3R for a solid, while a monatomic gas has Cv = (3/2)R?
Gas atoms have only kinetic energy, ½kBT in each of three directions. Atoms in a solid vibrate, so each direction has kinetic and potential energy terms, kBT in all, giving the classical high-temperature limit 3k_B T per atom and 3R per mole of atoms; quantum effects suppress the heat capacity at low temperatures.