Question

Physical Chemistry Question

whenever a gas expands--when we exhale, when a flask is opened, and so on--the gas undergoes an increase in entropy. A sample of methane gas of mass 25g at 250K and 185kPa expands isothermally and reversibly until its pressure is 2.5kPa. (a) Calculate the change in entropy of the gas. (b) What is the entropy change in the gas if it expands irreversibly to the same final temperature and pressure?

Also, find delta U, w, q, delta S surrounding, and delta S total

Answer 1

for ideal gas delta U= 0 ( since the operation is isothermal)

at constant temperature delS =-nR ln (P2/P1)

n= number of moles of methane , n = 25/16= 1.5625

where P2= final pressure and P1= initial pressure delS= -1.5625* 8.314* ln(2.5/185)=55.91 joules/K

Total entropy for a reversible proces= 0

entropy change of gas + entropy change of surroundings= 0

Entropy of surroundings= -55.91 joues/K

W= -nRT ln (P1/P2)= 1.5625*8.314*250* ln (185/2.5)=-16773.75 joules

delU= Q+W

delU= O ( constant temperature)

Q= -W= 16773.5 joules

for irreversible process delS= Q/T= 16773.5/250 =67.09 j/K