Question

16.2 kg of gas at 1.5 bar occupies a volume 2.5 m3. I the gas compressed isothermally of 1/3 times the initial volume. Find (i) the initial temperature (ii) the final temperature(iii) the work done and (iv) the heat transferred. Take R = 0.278 kJ/kg. K.

Answer 1

Explanation:

(i) Use ideal gas law.

PV = mRT

(1.5 bar × 100 kPa/bar) (2.5 m³) = (2 kg) (0.278 kJ/kg/K) T

T = 674 K

T = 401°C

(ii) The process is isothermal, so the final temperature equals the initial temperature.

(iii) Work for an ideal gas undergoing an isothermal process is:

W = mRT ln (V / V₀)

W = (2 kg) (0.278 kJ/kg/K) (674 K) ln (1/3)

W = -412 kJ

(iv) Heat transferred is Q = mCΔT. Since temperature is constant for an isothermal process, no heat is transferred.