Question

In Example 20.4, a Carnot refrigerator requires a work input of only 230 Jto extract 346Jof heat from the cold reservoir. Doesn’t this discrepancy imply a violation of the law of conservation of energy? Explain why or why not.

Short answer

Working of a refrigerator does not violate the law of conservation of energy.

Step-by-step solution

Total energy of an isolated system:

Law of conservation states that total energy for an isolated system is always constant.

The heat injected into the cold reservoir:Consider the given data as below.

The heat collected from the outside,${\mathrm{Q}}_{\mathrm{C}}=346\mathrm{J}$

The electrical energy,$\mathrm{W}=230\mathrm{J}$

Write the expression for heat delivered to the hot reservoir.

$\left|{\mathrm{Q}}_{\mathrm{H}}\right|=\left|{\mathrm{Q}}_{\mathrm{C}}\right|+\left|\mathrm{W}\right|$

The heat injected into the cold reservoir is ${\mathrm{Q}}_{\mathrm{H}}$, the heat collected from the outside is ${\mathrm{Q}}_{\mathrm{C}}$, and the electrical energy is W .

Substitute 346J forrole="math" localid="1663833249428" ${\mathrm{Q}}_{\mathrm{C}}$ and$230\mathrm{J}$ for W in the above equation to find

$$\begin{gathered} \left|{\mathrm{Q}}_{\mathrm{H}}\right|=230\mathrm{J}+346\mathrm{J} \\ =576\mathrm{J} \end{gathered}$$

This heat is liberated hot reservoir and energy is balanced.

Hence, working of a refrigerator does not violate the law of conservation of energy.