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Chapter 15: Problem 23

How much heat does a heat pump with a coefficient of performance of 3.0 deliver when supplied with \(1.00 \mathrm{kJ}\) of electricity?

Short Answer

Expert verified
Answer: The heat pump delivers 3.00 kJ of heat when supplied with 1.00 kJ of electricity.

Step by step solution

01

Understand the coefficient of performance of a heat pump formula

The coefficient of performance (COP) for a heat pump can be calculated using this formula: COP = Q_H / W, where Q_H is the heat delivered by the heat pump, and W is the work input (in our case, 1.00 kJ of electricity).
02

Use the given values to find the heat delivered

We are given the coefficient of performance (COP) as 3.0 and the work input (W) as 1.00 kJ. We can now use these values in the formula to find the heat delivered (Q_H): COP = Q_H / W => Q_H = COP * W
03

Calculate the heat delivered

Substitute the given values into the equation: Q_H = (3.0) * (1.00 kJ) Q_H = 3.00 kJ The heat pump delivers 3.00 kJ of heat when supplied with 1.00 kJ of electricity.

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Most popular questions from this chapter

Two engines operate between the same two temperatures of \(750 \mathrm{K}\) and \(350 \mathrm{K},\) and have the same rate of heat input. One of the engines is a reversible engine with a power output of \(2.3 \times 10^{4} \mathrm{W} .\) The second engine has an efficiency of \(42 \% .\) What is the power output of the second engine?
A heat engine uses the warm air at the ground as the hot reservoir and the cooler air at an altitude of several thousand meters as the cold reservoir. If the warm air is at \(37^{\circ} \mathrm{C}\) and the cold air is at $25^{\circ} \mathrm{C},$ what is the maximum possible efficiency for the engine?
Show that in a reversible engine the amount of heat \(Q_{C}\) exhausted to the cold reservoir is related to the net work done \(W_{\text {net }}\) by $$ Q_{\mathrm{C}}=\frac{T_{\mathrm{C}}}{T_{\mathrm{H}}-T_{\mathrm{C}}} W_{\mathrm{net}} $$
A reversible heat engine has an efficiency of \(33.3 \%\) removing heat from a hot reservoir and rejecting heat to a cold reservoir at $0^{\circ} \mathrm{C} .$ If the engine now operates in reverse, how long would it take to freeze \(1.0 \mathrm{kg}\) of water at \(0^{\circ} \mathrm{C},\) if it operates on a power of \(186 \mathrm{W} ?\)
An inventor proposes a heat engine to propel a ship, using the temperature difference between the water at the surface and the water \(10 \mathrm{m}\) below the surface as the two reservoirs. If these temperatures are \(15.0^{\circ} \mathrm{C}\) and \(10.0^{\circ} \mathrm{C},\) respectively, what is the maximum possible efficiency of the engine?
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