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### College Physics (Urone)

Book edition 1st Edition
Author(s) Paul Peter Urone
Pages 1272 pages
ISBN 9781938168000

# Grocery store managers contend that there is less total energy consumption in the summer if the store is kept at a low temperature. Make arguments to support or refute this claim, taking into account that there are numerous refrigerators and freezers in the store.

Total energy consumption during summer can be reduced by keeping the temperature of the store low.

See the step by step solution

## Step 1: Explain how the efficiencies of refrigerator is calculated.

The efficiency of refrigerators is determined by the coefficient of performance. It is calculated as follows:

$$\begin{array}{l}CO{P_{hp}} = \frac{{{Q_h}}}{W}\\CO{P_{ref}} = \frac{{{Q_c}}}{W}\\W = {Q_h} - {Q_c}\end{array}$$

Here, $$CO{P_{hp}}$$is the coefficient of performance of the heat pump, $${Q_h}$$is amount of heat transfer into the warmer space and $$W$$ is the work input. $$CO{P_{ref}}$$ is the coefficient of performance of refrigerator and $${Q_c}$$ is the heat in the environment.

## Step 2: Explain how the efficiency depends on temperature in the store.

The expressions of coefficient of performance indicates that it is inversely proportional to the work output. In a Carnot engine,

$$\begin{array}{l}{Q_c} = {T_c}\\{Q_h} = {T_h}\\W = {T_h} - {T_c}\end{array}$$

Here, $${T_c}$$ is the temperature of the refrigerator and $${T_h}$$ is the temperature at the store. If the temperature at the store is kept low, the difference between the temperature in the refrigerator and the temperature in the store will be reduced. As a result, the work input required also decreases. Thus, total energy consumption is lowered.

Thus, energy consumption in the store can be reduced by keeping the store at low temperature.