Question

Demonstrate that the power requirement for compressing a gas is smaller the more complex the gas. Assume fixed values of number of moles, n, efficiency, T1, P1 and P2, adn that the gas is ideal with constant heat capacities.

Answer 1

Suppose the gas follows polytropic process in general, such that

Where n= = C_p/Cv for adiabatic process

Initial temperatue of gas = T₁

Initial pressure of gas = P₁

Final pressure of gas = P₂

So, we can write

.............................................................(1)

Now as we know that for polytropic process, work done is calculated as

Where, n₁ is the number of moles

Put the value of T₂ from equation 1, we have

Here efficiency of compressure is , therefore net power required will be