Question

3.75 moles of ideal fas with CV,m=3/2R undergoes the transformations described in the following list from an initial state described by T=298K and P=4.50 bar.

c)The gas undergoes an expansion against a constant external pressure of zero bar until the final pressure is one third its initial value. Find S

Answer #1

We know, C_{p,m} - C_{v,m} = R

=> C_{p,m}= R + C_{v,m}

=> C_{p,m} = R + 3/2 R

=> C_{p}_{,m} = 5/2 R

Given , P_{f} = 1 bar , P_{i} = 3 bar ,
T_{f} = 298 K , T_{i} = 298 K, n = 3.75 moles

Now,

S = - nR ln
P_{f} /P_{i} + n C_{p,m}ln T_{f} /
T_{i}

=> S = -3.75 mol *
8.314 J mol^{-1}K^{-1} * ln(1/3) + 3.75 mol * (5/2)
* 8.314 Jmol^{-1}K^{-1} * ln 1

=> S = -31.1775 *
ln( 0.33) JK^{-1} + 0

=> S = -31.1775 * -
1.1086 JK^{-1}

=> **S = 34.6
JK ^{-1}**

or we can solve by another way as, P_{external} = 0 ,
T =0

so, S = - nR ln
P_{f} / P_{i} = - 3.75 mol * 8.314
Jmol^{-1} K^{-1} * ln (1 /3) = **34.6
JK ^{-1}**

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