Nitrogen gas is contained in a piston/cylinder arrangement as shown below. The f

Question

Nitrogen gas is contained in a piston/cylinder arrangement as shown below. The frictionless (freely moving) piston keeps the nitrogen at a constant pressure of 200 kPa. Initially, the nitrogen is at 20 degree C and occupies a volume of 0.01 m^3 (State 1). Heat is transferred until the nitrogen reaches 250 degree C (State 2). Assume ideal gas with the constant specific heats given below to find the following: The work done in kJ. Clearly indicate whether work is done on or by the system. The heat transferred in kJ. Clearly indicate the direction of heat transfer (into or out of the system). Data for Nitrogen: R = 0.2968 kJ/(kg. K), C_p0 = 1.042 kJ/(kg. K), C_v0 = 0.7452 kJ/(kg. K)

Explanation / Answer

U = internal energy

H = enthalpy

Q = Heat

W = work done

V = volume

P = pressure

T = temperature

H = CpdT and U = CvdT

also, H = U + PdV

CpdT = CvdT + PdV

Cp(T2 - T1) = Cv(T2 - T1) + P(V2 - V1)

T2 = 250+273 = 523 K

T1 = 293 K

V1 = 0.01 m3

substitute values to get V2 = 0.35132 m3

Therefore, work done = PdV = P(V2 - V1)

W = 200*(0.35132 - 0.01)

W = 68.264 kJ

Since work is done by the system it will be positive

U = -Q + W

Q is added so it will be negative and work is extracted so it will be positive.

U = CvdT = 171.396 kJ/kg

Q = -171.396 + 68.264

Q = -103.132 kJ

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