A heat engine operates between two thermal reservoirs at 800 and 20"C. One-half of the work output of the heat engine is used to drive a Camot heat pump that removes heat from the cold surroundings at 2°C and transfers it to a house maintained at 22 C. If the house

is losing heat at a rate of 95,000 kJ/h.

a) Define the following

i. Heat

Thermal reservoir

[2]

Heat engine iv. Heat pump

(2)

b) Determine

12)

[2]

i. The COP for the Carnot heat pump ii. The rate of work output for the heat engine.

[3]

The minimum rate at which heat must required to keep the house at 22°C.

[51 be

1 answer

a) Definitions:

i. Heat: Heat is a form of energy that is transferred between two substances or systems as a result of a temperature difference.

Thermal reservoir: A thermal reservoir is a large body or system that can provide an infinite amount of heat or absorb an infinite amount of heat without changing its own temperature significantly.

Heat engine: A heat engine is a device that transforms heat energy into mechanical work in a cyclic process.

Heat pump: A heat pump is a device that uses mechanical work to transfer heat from a low-temperature reservoir to a high-temperature reservoir.

b) Calculations:

i. The coefficient of performance (COP) for a Carnot heat pump can be calculated using the formula COP = Th/(Th - Tc), where Th is the temperature of the hot reservoir and Tc is the temperature of the cold reservoir. In this case, Th = 22°C and Tc = 2°C. Plugging in the values into the formula, we get COP = 22/(22 - 2) = 22/20 = 1.1.

ii. The rate of work output for the heat engine can be calculated using the formula W = Qh - Qc, where Qh is the heat absorbed from the hot reservoir and Qc is the heat rejected to the cold reservoir. Since we know that one-half of the work output is used to drive the heat pump, the work output of the heat engine is 2 times the work input of the heat pump. Therefore, W = 2 * (Qh - Qc).

iii. The minimum rate of heat required to keep the house at 22°C can be calculated using the formula Qh = W + Qc, where Qh is the heat absorbed from the hot reservoir, W is the work input to the heat pump, and Qc is the heat rejected to the cold reservoir. In this case, Qh = 2 * Qc.

Please provide the inputs for Qh, Qc, or any other relevant information to further calculate the answers.