Air is contained in a variable-load piston{cylinder device equipped with a stirring paddle wheel. Initially, air is at 400 kPa and 17 C. The paddle wheel is now turned by a motor until 75 kJ:kg of work has been transferred to air. Model the air as an ideal gas with constant speci c heats 1 and calculate the amount of heat transfer per unit mass that is needed to maintain a constant air temperature while allowing the gas volume to triple.

Question:

Calculate the required amount of heat transfer, in kJ/kg.

16.44KJ/Kg

Explanation:

Given

P1 = Initial Pressure = 400KPa

T1 = Initial Temperature = 17°C = 17 + 273 = 290

W,out = Workdone by peddle wheel = 75KJ/Kg

Final Volume = V2 = 3V1

R = Gas Constant of air = 0.287

Given that the system is a close system, the change in energy is given by

∆E = E,in - E,out Energy Balance

∆W = W,in - W,out

The boundary work could be defined as follows:

W,b = RT ln(V2/V1)

W,b = 0.287 * 290 * ln(3V1/V1)

W,b = 83.23 * ln(3)

W,b = 91.44 KJ/Kg W,in

∆W = W,in - W,out

∆W = 91.44 - 75

∆W = 16.44KJ/Kg

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