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.

(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