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.

the ima (higher than 1m) will be greater than the ima with the height of 1m.