A 1.50-mol sample of ideal gas undergoes an irreversible isothermal expansion at
ID: 1060498 • Letter: A
Question
A 1.50-mol sample of ideal gas undergoes an irreversible isothermal expansion at 298 K. Its initial pressure is 10.0 bar. It expands against a constant external pressure of 1.00 bar until mechanical equilibrium is reached. Determine values of delta S and delta S_surr for the process. Repeat the problem under conditions in which the gaseous system undergoes the same change of state, but the external pressure is zero. (This is known as a 'free expansion, ' or expansion into a vacuum.) Assume a mechanical device is in place that stops the expansion when the volume reaches the same value as in the first part of the problem.Explanation / Answer
for irrversiblle isothermal expansion , deltaU=0, Q+W=0 and W= -Q
Q= -Pext*(V2-V1), V1= nRT/P= 1.5*0.0821*298/10 = 3.67 L and V2= 1.5*0.0821*298/1 =36.69 L
W = -1*(36.69-3.67) atm.L =-33.02 atm.L = -33.02*101.3 Joules =-3345 joules
Q= 3345 joules entropy change of system= Q/T= 3345/298 =11.22 Joules/K
that of surroundingns =-11.22 joules/K
2. Work done against free expansion = 0 and hecne Q=0 and hence entropy change = 0
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