Total entropy change in a polytropic compressing of methane

Example 3.2 Total entropy change in a polytropic compressing of methane We compress methane from an initial state at 100 kPa, 300 K, and 20 m3 to 250 kPa and 400 K. The compression process is polytropic (PVa = constant). The average heat capacity of methane is Cpw = 40.57 J/(mol K). Estimate the supplied work and the total entropy change if the surroundings are at 290 K. 

Assume that the methane is an ideal gas. The heat capacity is constant. 

The surface work of the poly tropic compression becomes 

From the energy balance, we estimate the heat discharged to surroundings 

Since the surroundings undergo a reversible isothermal process, we have 

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Example 3.2 Total entropy change in a polytropic compressing of methane... 

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