Question

Methane at 10 mpa and 300 k is heated at constant pressure until its volume has increased by 80 percent. determine the final temperature using the ideal gas equation of state and the compressibility factor. which of these two results is more accurat

Answer 1

When you assume that the gas is behaving ideally, the gas molecules are very far from each other that they do not have any intermolecular forces. If it behaves this way, you can assume the ideal gas equation:

PV = nRT, where

P is the pressure
V is the volume
n is the number of moles
R is a gas constant
T is the absolute temperature

When the process goes under constant pressure (and assuming same number of moles),

P/nR = T/V = constant, therefore,

T₁/V₁=T₂/V₂

If V₂ = V₁(1+0.8) = 1.8V₁, then,

T₂/T₁ = 1.8V₁/V₁

Cancelling V₁,

T₂/300=1.8
T₂ =540 K

If you do not assume ideal gas, you use the compressibility factor, z. The gas equation would now become

PV =znRT

However, we cannot solve this because we don't know the value of z₁ and z₂. There will be more unknowns than given so we won't be able to solve the problem. But definitely, the compressibility factor method is more accurate because it does not assume ideality.