Question

In Problems $65$through $68$you are given the equation(s) used to solve a problem. For each of these, you are to

a. Write a realistic problem for which this is the correct equation(s).

b. Finish the solution of the problem.

$4.0={\mathrm{Q}}_{\mathrm{C}}/{\mathrm{W}}_{\text{in}}$

${\mathrm{Q}}_{\mathrm{H}}=100\mathrm{J}$

Short answer

a. The coefficient is $4.0$and heat is $100\mathrm{J}$.Work done is needed.

b. The value of work done$20\mathrm{J}$.

Step-by-step solution

Explanation (part a)

a.

"The environment received $100\mathrm{J}$of heat from a refrigerator with a performance coefficient of $4.0$.

Look for the work that has been done to the system."

Problem with solution (part b)

b.

The relationship between work and heat emitted from the cold reservoir can be established using the first supplied equation as follows:

$4.0=\frac{{\mathrm{Q}}_{\mathrm{c}}}{{\mathrm{W}}_{\mathrm{in}}}$

$\Rightarrow {\mathrm{Q}}_{\mathrm{c}}=4{\mathrm{W}}_{\mathrm{in}}$

We have come a long way since the first refrigerator law was enacted.

${\mathrm{Q}}_{\mathrm{h}}={\mathrm{W}}_{\mathrm{in}}+{\mathrm{Q}}_{\mathrm{c}}$

$={\mathrm{W}}_{\mathrm{in}}+4{\mathrm{W}}_{\mathrm{in}}$

$=5{\mathrm{W}}_{\mathrm{in}}$

The work input is,

role="math" localid="1650280024693" ${\mathrm{W}}_{\mathrm{in}}=\frac{{\mathrm{Q}}_{\mathrm{h}}}{5}$

role="math" localid="1650280033690" $=\frac{100J}{5}$

$=20\mathrm{J}$