N2 gas fills a flexible container with an initial volume of 0.05 m3, a temperature of 30oC, and a pressure of 800 kPa. The N2 gas is to expand in an isothermal manner until the pressure is 100 kPa.

Question

(a) Determine the amount of heat transfer required for this process in order to maintain an isothermal nature.
(b) Develop a computer model to simulate this process, and then plot the amount of heat transfer required for an isothermal process for final pressures ranging between 100 kPa and 600 kPa.
Given: N2; T1 = T2 = 30oC; P1 = 800 kPa; V1 = 0.05 m3; P2 = 100 kPa
Assume: N2 behaves as an ideal gas with constant specific heats: cv = 0.743 kJ/kg-K; R = 0.2968 kJ/kg-K; ?KE = ?PE = 0.

Answer 1

Solution: The First Law for closed systems reduces to

Q – W = m (u2 – u1) = mcv(T2 – T1) = 0

For an ideal gas undergoing an isothermal process: pV = constant

So, W=

(a) Because P1V1 = P2V2, we can find V2 = 0.40 m3

W = 83.2 kJ

And Q = W = 83.2 kJ



(b) For the pressure range given:





The amount of heat transfer to maintain isothermal expansion is less for less expansion (i.e., a higher final pressure).