Question

Calculate the change in entropy (in J/K) when 38.7 g of nitrogen gas is heated at a constant pressure of 1.50 atm from 22.9 ºC to 88.2 ºC. (The molar specific heats are Cv is 20.8 J/(mol-K) and Cp is 29.1 J/(mol-K) .)

Answer 1

Given , T_i = 22.9⁰C = (22.9 +273) K = 295.9 K , T_f = 88.2⁰C = ( 88.2 + 273) K = 361.2 K

mass of nitrogen gas (N₂) = 38.7 ,

so moles of N₂ gas = mass of N₂ / molar mass of N₂ = (38.7g / 28g /mol) = 1.38 mol

We have the relation as--

Tds = dh - vdp

At constant pressure, dp =0

so Tds = dh
=> ds = dh/T

=> ds = (C_p/T)dT

=> S = nC_p x ln(Tf / Ti)

=> S = nC_p x ln(Tf / Ti)

=>S = 1.38 mol x 29.1 J/mol K *ln(361.2 K /295.9 K)

=> S = 40.158 x ln(1.221) J/K

=> S = 40.158 x 0.199 J/K

=> S =7.99 J/K