A Carnot engine has a power output of 148 kW. The engine operates between two reservoirs at 17◦C and 727◦C. How much thermal energy is absorbed each hour? Answer in units of J.

Question

Physics

Molly Fletcher

23 November, 11:47

A Carnot engine has a power output of 148 kW. The engine operates between two reservoirs at 17◦C and 727◦C. How much thermal energy is absorbed each hour? Answer in units of J.

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Answers (1)

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Mcclain · Answer 1

The thermal Energy absorbed each hour = 750420 kJ

Explanation:

Efficiency of a Carnot engine = W/Q = (Th-Tc) / Th ... Equation 1.

W/Q = (Th-Tc) / Th

making Q the subject of the equation above,

Q = W (Th) / (Th-Tc) ... Equation 2

Where Q = input power, W = output power, Th = temperature of the hot reservoir, Tc = Temperature of the cold reservoir.

Given: W = 148 kW, Th = 727 °C = 727 + 273 = 1000 K, Tc = 17 °C = 17 + 273 = 290 K.

Substituting these values into equation 2,

Q = 148 (1000) / (1000-290)

Q = 148000/710

Q = 208.45 kw

The thermal Energy absorbed each hour = 208.45 kW * 3600 s

The thermal Energy absorbed each hour = 750420 kJ