Question

2.15 mol of an ideal gas with *C*V,m=3*R*/2
undergoes the transformations described in the following list from
an initial state described by *T*=350.K and
*P*=5.00bar.

1) The gas undergoes a reversible adiabatic expansion until the final pressure is one-fourth its initial value.

2) The gas undergoes an adiabatic expansion against a constant external pressure of 1.25 bar until the final pressure is one-fourth its initial value.

3)The gas undergoes an expansion against a constant external pressure of zero bar until the final pressure is equal to one-fourth of its initial value.

a) Calculate *q* for each process. (q1,q2,q3)

b) Calculate *w* for each process. (w1,w2,w3)

c) Calculate Δ*U* for each process. (Δ*U1,*
Δ*U2,* Δ*U3)*

d) Calculate Δ*H* for each process. (Δ*H1,*
Δ*H2,* Δ*H3)*

e) Calculate Δ*S* for each process. (Δ*S1,*
Δ*S2,* Δ*S3)*

Answer #1

**Process 1**.

a) In the adiabatic process, there will be no heat exchange between the system and surroundings.

i.e. **q1 = 0**

b) w1 = n * C_{V,m} * (T2 - T1)

T2/T1 = (P2/P1)^{(-1)/}

Here,
= 5/3 (since C_{V,m} = 3/2 R)

Therefore, T2 = 350 K * (1/4)^{2/5} = 201 K

Hence, **w1** = 2.15 mol * 3/2 * 8.3145 J
mol^{-1} K^{-1} * (201-350) K = **-3.995
kJ**

c) For an adiabatic reversible process, w = U

Therefore, **
U1 = -3.995 kJ**

d) H = 5/3 U (since H = 5/2 R and U = 3/2 R)

Therefore, **
H1** = 5/3 * -3.995 kJ = **-6.658 kJ**

e) **
S1 = 0** (since q1 = 0, reversible process)

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