Helium gas contained in a piston cylinder assembly undergoes an isentropic polytropic process from the given initial state with P1 = 0.02 bar, T1 = 200 K to the final state with P2 = 0.14 bar. Determine the work and heat transfer (per unit mass) involved in this process.

Heat transfer during the process = 0

Work done during the process = - 371.87 KJ

Explanation:

Initial pressure = 0.02 bar

Initial temperature = 200 K

Final pressure = 0.14 bar

Gas constant for helium R = 2.077

This is an isentropic polytropic process so temperature - pressure relationship is given by the following formula,

=

Put all the values in above formula we get,

⇒ =

⇒   = 1.74

⇒ = 348.72 K

This is the final temperature of helium.

For isentropic polytropic process heat transfer to the system is zero.

⇒ ΔQ = 0

Work done W = m × ( - ) ×

⇒ W = 1 × ( 200 - 348.72 ) ×

⇒ W = 371.87 KJ

This is the work done in this process. here negative sign shows that work is done on the gas in the compression of gas.

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