One mole of an ideal monatomic gas (γ = 5/3) expands adiabatically and cools from 60 K to 50 K. Find the work done by the gas. Take R = 8.3 J mol⁻¹ K⁻¹.
Options

Question

One mole of an ideal monatomic gas (γ = 5/3) expands adiabatically and cools from 60 K to 50 K. Find the work done by the gas. Take R = 8.3 J mol⁻¹ K⁻¹.

G1 Physics · Accepted Answer

Step 1: Adiabatic process means Q = 0. Step 2: First law in work-by-system convention: ΔU = Q − W, so W = −ΔU. Step 3: For one mole of monatomic ideal gas, Cᵥ = 3R/2. Step 4: W = nCᵥ(Tᵢ − T𝒇) = 1 × (3/2 × 8.3) × (60 − 50). Step 5: W = 12.45 × 10 = 124.5 J. Positive sign means work by the expanding gas. Final answer: 124.5 J (Option C).