Question

Questions #19 and 20:

Part 1 of 2: A Carnot engine has a power output of 122 kW. The engine operates between two reservoirs at 9 °C and 458 °C. How much thermal energy is absorbed each hour? Answer in units of J.

Part 2 of 2: How much thermal energy is lost per hour? Answer in units of J.

Answer 1

(1) The thermal energy absorbed by the Carnot engine is 7.15 x 10⁸ J.

(2) The thermal energy lost per hour by the Carnot engine is 2.75 x 10⁸ J.

Thermal energy entering the heat engine

The thermal energy absorbed by the heat engine is calculated as follows;

$Q_h = \frac{P\Delta t}{1 - T_c/T_h}$

where;

• Tc is the temperature of the cold reservoir = 9 + 273 = 282 K
• Th is the temperature of the hot reservoir = 458 + 273 = 731 K

$Q_h = \frac{(122,000) \times (3600)}{1 - \frac{282}{731} } \\\\Q_h = 7.15\times 10^8 \ J$

Thermal energy lost by the heat engine

The thermal energy lost per hour by the heat engine is calculated as follows;

$Q_c = Q_h - P\Delta t\\\\Q_c = (7.15 \times 10^8 )\ - \ (122,000 \times 3600)\\\\Q_c = 2.75 \times 10^8 \ J$

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