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Physics

1st Edition

Walker

ISBN: 9780133256925

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Page 391: Practice Problems

Exercise 4

Step 1

1 of 3

### Knowns

– Amount of work done $W = 1250text{ J}$

– Amount of heat lost to cold reservoir $Q_{text{c}} = 5250text{ J}$

Step 2

2 of 3

### Calculation

The energy that goes into a heat engine also goes out so we write:

$$
begin{align*}
Q_{text{h}} = Q_{text{c}} + W
end{align*}
$$

Now we use the definition of efficiency to find its value:

$$
begin{align*}
e = frac{W}{Q_{text{h}}} = frac{W}{Q_{text{c}} + W}
end{align*}
$$

Plugging in the numbers:

$$
begin{align*}
e = frac{1250text{ J}}{5250text{ J} + 1250text{ J}} = frac{1250}{6500} = 19.23 , %
end{align*}
$$

Result

3 of 3

The efficiency of the engine is $e = 19.23 %$

Exercise 5

Step 1

1 of 3

### Knowns

– Amount of work done $W = 340text{ J}$

– Amount of heat lost to cold reservoir $Q_{text{c}} = 870text{ J}$

Step 2

2 of 3

### Calculation

The energy that goes into a heat engine also goes out so we write:

$$
begin{align*}
Q_{text{h}} = Q_{text{c}} + W
end{align*}
$$

Now we use the definition of efficiency to find its value:

$$
begin{align*}
e = frac{W}{Q_{text{h}}} = frac{W}{Q_{text{c}} + W}
end{align*}
$$

Plugging in the numbers:

$$
begin{align*}
e = frac{340text{ J}}{870text{ J} + 340text{ J}} = frac{340text{ J}}{1210text{ J}} = 28,1 , %
end{align*}
$$

Result

3 of 3

The efficiency of the engine is $e = 28.1 , %$

Exercise 6

Step 1

1 of 3

### Knowns

– Amount of heat received from the hot reservoir $Q_{text{h}} = 690text{ J}$

– Amount of heat lost to cold reservoir $Q_{text{c}} = 430text{ J}$

Step 2

2 of 3

section*{Calculation}
begin{enumerate}[a)]
item
The energy that goes into a heat engine also goes out so we write:
begin{align*}
Q_{text{h}} = Q_{text{c}} + W
end{align*}
Rearranging for work we have:
begin{align*}
W = Q_{text{h}} – Q_{text{c}}
end{align*}
Plugging in the numbers we get:
begin{align*}
W = 690text{ J} – 430text{ J} = 260text{ J}
end{align*}
item
Now we use the definition of efficiency to find its value:
begin{align*}
e = frac{W}{Q_{text{h}}} = frac{Q_{text{h}} – Q_{text{c}} }{Q_{text{h}}} = 1 – frac{Q_{text{c}}}{Q_{text{h}}}
end{align*}
Plugging in the numbers:
begin{align*}
e = 1 – frac{430text{ J}}{690text{ J}} approx 37.68 , %
end{align*}
end{enumerate}

Result

3 of 3

begin{enumerate}[a)]
item
the work done by the engine is $W = 260text{ J}$
item
the efficiency of the engine is $e = 37.68 , %$
end{enumerate}

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