At constant volume, 4 mol of an ideal gas when heated from 300 K to 500K changes its internal energy by 5000 J. The molar heat capacity at constant volume is _______. (Round off to the nearest integer)

Solution

Chemistry ma’am · 3 steps

At constant volume no work is done, so Δ U = nCᵥΔ T gives Cᵥ in one line.

1. Why constant volume helps. At constant volume the gas does no work, so the heat supplied equals Δ U. For an ideal gas this change depends only on the moles and the temperature change.

   Δ U = nCᵥΔ T ⇒ Cᵥ = (Δ U)/(n Δ T)

2. Put in numbers. Δ T = 500 - 300 = 200 K and n = 4 mol. So Cᵥ = 5000/(4 × 200) = 5000/800 = 6.25 J K⁻¹ mol⁻¹.
3. So. The molar heat capacity at constant volume is 6.25 J K⁻¹ mol⁻¹, which rounds to 6.

The common slip: 25. Leaving out the 4 mol gives 5000/200 = 25, which is the heat capacity of the whole sample, not the molar value.

The idea to keep. Molar heat capacity is per mole and per kelvin, so divide the energy by both n and Δ T. Use the change in temperature, never a single temperature.

Answer from the NTA final answer key. Solution by PrepWiser.