4-81 Air is contained in a cylinder device fitted with a piston-cylinder. The pi

Question

4-81 Air is contained in a cylinder device fitted with a piston-cylinder. The piston initially rest on a set of stops, and a pressure of 300 kPa is required to move the piston. Initially, the air is at 100 kPa and 27 degrees Celsius and occupies a volume of 0.4 m^3. Determined the amount of heat transferred to the air, in kJ, while increasing the temperature to 1200 K. Assume air has the constant specific heats evaluated at 300 K.
Answer: 340kJ
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Explanation / Answer

As temperature of air in cylinder rises, its pressure also rises. Until the pressure reaches 300 kPa, piston will not move and we'll have to consider constant volume heating. From 300 kPa onwards until temperature reaches 1200 K, we'll have to consider constant pressure heating.

Specific heat at constant pressure for air at 300 K, Cp = 1.005 kJ/kg-K

Specific heat at constant volume for air at 300 K, Cv = 0.718 kJ/kg-K

Using pV = mRT we get mass of air m = pV/RT = (100*103)*0.4/(287*(27+273)) = 0.4645 kg

For constant volume heating, P/T = constant.

So, 100/(27+273) = 300/T2

T2 = 900 K

For constant pressure heating, V/T = constant.

0.4/900 = V3/1200

V3 = 0.5333 m3

Total change in internal energy U = mCv(T3-T1) = 0.4645*0.718*(1200-300) = 300 kJ

Net work done W = P2(V3 - V2) = 300*103 * (0.5333 - 0.4) = 40 kJ

Q - W = U

Heat transfer Q = W + U = 300 kJ + 40 kJ = 340 kJ

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