Question

A stream of methane gas at 25 bar and 100°C flows into a container that contains methane gas initially at 1 bar and 100°C until the pressure in the container reaches 25 bar. If the volume of the container is 200 L, calculate the final temperature of the gas in the tank. Assume methane is an ideal gas with constant Cp

Answer 1

Since Methane is assumed an ideal gas, we need to know its moles in each streams.

Therefore, we can use the ideal gas law to find the mole in the container by:  

P V=nRT         ⇒     n=PV/R T

n=no of moles of the gas = mass/molar mass

Molar mass o f CO2=44g/mol, mass = 44g

P= 25bar = 101000X25Pa=2.5x106Pa

V = 20L = 20dm3 = 0.02m3

T=100C=373K

R=8.314J/mol.K

n1= 2.5x106Pa x 0.02m3 / 8.314J/mol.K x 373K

n1 = 16.1mols

Similarly for stream 2, we have n2 which is

P=1bar = 100000Pa

T= 100C= 373K

V=200L = 0.02m3

n2= 1x105Pa x 0.02m3 / 8.314J/mol.K x 373K

n1 = 0.645mol

So the new stream is an addition of these two streams of methane which has

n3 = n1 + n2 =16.75mols of methane

T=?

V=200L=0.02m3

P = 25Bar = 2.5x106Pa

T= PV/nR

T = 2.5x106Pa x 0.02m3 / 16.75 x 8.314

T=359K

So the final temperature of the gas in the tank is 359K