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,mln T_f / T_i

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