Question

1 kg of oxygen is heated from 20 to 120°C. Determine the amount of heat transfer required when this is done during a (a) constant-volume process and (b) isobaric process.

Answer 1

(a) At constant-volume, Q = 66.7kJ

(b) At isobaric condition, Q = 92.7kJ

Explanation:

The specific heats of oxygen at the average temperature of (20+120)/2 = 70°C = 343 K are

Cp = 0.927  kJ/kg.K

Cv = 0.667 kJ/kgK

We take the oxygen as the system. This is a closed system since no mass crosses the boundaries of the  system. The energy balance for a constant-volume process can be expressed as

ΔE (system) = E(in) - E(out)

and

Q(in) = ΔH = mCp x (T₂ - T₁)

since ΔU + Wb = ΔH during a constant pressure quasi-equilibrium

process. Substituting for both cases,

(a)

Qin,V =const = mCv  (T2 - T1 )

                      = (1kg)(0.667 kJ/kg.K)(120 - 20)K

                      = 66.7kJ

(b)

Qin,P=const = mCp  (T2 - T1  )

                     = (1kg)(0.927 kJ/kg.K)(120 - 20)K

                     = 92.7kJ