In a closed system one kilogram of carbon dioxide (CO_2) is expanded reversibly from 30 degree C and 200 kPa to 100 kPa pressure. If the expansion is polytropic with n = 1.27, determine the total work, the change in total internal energy, and the total heat transferred in [kJ], Note that for CO_2, R = 188.9 J/kg. K and c_v = 655 J/kg. K. W = -29.05 kJ, DeltaU = -27.19 kJ, Q = 1.860 kJ

the total work W =  29.05 kJ

the change in total internal energy is

the  total heat transferred in [kJ] is  Q = 1.860 kJ

Explanation:

Given that

mass of carbon dioxide in the closed system = 1 kg

Temperature = (273+30 ) K = 303 K

Pressure

Pressure

polytropic expansion n = 1.27

Note that we are also given the following data set:

R = 188.9 J/kg.K

c_v = 655 J/kg.K

So; for a polytropic process ;

Since the system does not follow the first order of thermodynamics; To calculate the total work by using the expression:

W =  29048.62222 J

W =  29.05 kJ

Thus, the total work W = 29.05 kJ

The change in internal energy can be expressed  by the formula:

Hence; the change in total internal energy is

Finally; to determine the  total heat transferred in [kJ]; we go by the expression for the first order of thermodynamics which say:

Total Heat Q = ΔU + W

Q = (-27.19 + 29.05)kJ

Q = 1.860 kJ

Hence; the  total heat transferred in [kJ] is  Q = 1.860 kJ

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