Question

A cylinder/piston contains 1 kg methane gas at 100 kPa, 20°C. The gas is compressed reversibly to a pressure of 800 kPa. Calculate the work required if the process is

a.  Adiabatic

b.  Isothermal

c.  Polytropic, with exponent n = 1.15 

Answer 1

C.V. Methane gas of constant mass m₂ = m₁ = m and reversible process.

(a) Process: ₁Q₂ = 0 => s₂ = s₁

thus isentropic process s = const and ideal gas gives relation

(b)  Process: T = constant. For ideal gas then u₂ = u₁  and

Energy eq. gives ₁W₂ = ₁Q₂ and ∫ dQ/T = ₁Q₂/T

with the entropy change found 

=> ₁W₂ = ₁Q₂ = mT(s₂ - s₁) = -mRT ln(P₂/P₁)

= -0.51835× 293.2 ln(800/100) = -316.0 kJ

(c)  Process: Pvⁿ = constant with n = 1.15 ;

The T-P relation is given