Question

A piston cylinder device contains a mixture of 0.2 kg of H2 and 1.6 kg of N2 at 100 kPa and 300K. Heat is now transferred to the mixture at constant pressure unitl the volume is doubled. Assuming constant specific heats at the average temperature (the constant pressure specific heats of H2 and N2 are 14.501 kJ/kg°K and 1.049 kJ/kg°K, respectively), determine: a) the heat transfer. b) the entropy change of the mixture.

Answer 1

See system as total pressure condition
PV = nRT
PV/T = nR = constant
P1V1/T1 = P2V2/T2, P1 = P2
T2/T1 = V2/V1, final temperature can be solved

Entropy change,
Tds = du + pdv
ds = du/T + (p/T)dv, dh = c_v*dT, p/T = R/v
Δs = c_v ln(T2/T1) + R ln(v2/v1)
ΔS = n*[ c_v ln(T2/T1) + R ln(v2/v1) ]

Total entropy change,
Assume Dalton model, V_N2 = V_H2 as particles occupied very small volume of cylinder.
ΔS = ΔS_N2 + ΔS_N2
ΔS = n_H2*[ c_v_H2*ln(T2/T1) + R ln(v2/v1) ] + n_N2*[ c_v_N2* ln(T2/T1) + R ln(v2/v1) ]
Moles, specific heat, volume and temperature comparation are knowns.