7 mol of a certain monoatomic ideal gas undergoes a temperature increase of 40 K at constant pressure. The increase in the internal energy of the gas in this process is :
(Given R=8.3 JK⁻¹ mol⁻¹ )

Solution

Physics sir · 4 steps

Internal energy depends only on temperature, so use Cᵥ even though the pressure is constant.

1. Why Cv. For an ideal gas, internal energy depends only on temperature. So Δ U = nCᵥΔ T in every process, including this constant-pressure one.
2. Monoatomic gas. A monoatomic gas has 3 degrees of freedom, so Cᵥ = 3/2R.

   Δ U = nCᵥΔ T = 7 × 3/2 × 8.3 × 40

3. Put in numbers. 7 × 8.3 = 58.1, then 58.1 × 40 = 2324, and 2324 × 1.5 = 3486.
4. So. The internal energy rises by 3486 J, which is option (b).

The idea to keep. For an ideal gas, Δ U = nCᵥΔ T in any process. Cₚ only enters when you want the heat supplied at constant pressure.

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