Air is located in a piston-cylinder device. Initially, the air is 20oC and the pressure is 200 kPa, while the volume is 0.1 m3.

Question

(a) The air is heated at constant pressure until the volume is 0.3 m3. Determine the heat transfer for the process.
(b) For the same initial conditions, use your piston-cylinder device model to generate data, and plot the heat transferred for an isobaric expansion to volumes ranging from 0.15 m3 to 0.50 m3.
Given: Air; T1 = 20oC = 293 K; P1 = P2 = P = 200 kPa; V1 = 0.1 m3; V2 = 0.3 m3
Assume: Air behaves as an ideal gas with variable specific heats (expect a large temperature change): R = 0.287 kJ/kg-K; ?KE = ?PE = 0.

Answer 1

Solution: The First Law for closed systems reduces to

Q – W = m (u2 – u1)

For a constant pressure process, the moving boundary work is W = P (V2 – V1)

(a) W = (200 kPa)(0.3-0.1)m3 = 40.0 kJ

m = P1V1/RT1 = 0.2378 kg

T2 = P2V2/mR = 879 K

For air: u1 = 209.06 kJ/kg; u2 = 657.12 kJ/kg

Q = (0.2378 kg) (657.12 – 209.06) kJ/kg + 40 kJ = 147 kJ



(b) Using the same equations, the heat transfer for the final pressure range is



The graph is not quite linear, due to the variability of the specific heats of the air with the large temperature change.