Suppose that a heat engine operates with a hot source at a temperature of 485 oC and a cold sink at 42 oC. What is the maximum amount of work the engine is capable of performing if 9.75 kJ of heat are extracted from the hot source?

W = - 10.5943 KJ, work is negative because it is carried out by the system towards the surroundings.

Explanation:

heat engine:

∴ Th = 485°C

∴ Tc = 42°C

∴ Qh = 9.75 KJ ... heat from hot source

first law:

∴ ΔU = Q + W = 0 ... cyclic process

⇒ Q = - W

∴ Q = Qh + Qc = Qh - ( - Qc)

∴ Qc: heat from the cold source (-)

⇒ Qh - ( - Qc) = - W ... (1)

⇒ Qc/Qh = - Tc/Th ... (2)

from (2):

⇒ Qc = - (Tc/Th) (Qh) = - (42°C/485°C) (9.75 KJ)

⇒ Qc = - 0.8443 KJ

replacing in (1):

⇒ - W = 9.75 KJ - ( - 0.8443 KJ)

⇒ - W = 10.5943 KJ