To determine the efficiency of a device that takes in [tex]\( 400 \, J \)[/tex] of heat and does [tex]\( 120 \, J \)[/tex] of work while giving off [tex]\( 280 \, J \)[/tex] of heat, we can use the formula for efficiency:
[tex]\[ e = \frac{W_{\text{total}}}{Q_{\text{in}}} \][/tex]
where:
- [tex]\( W_{\text{total}} \)[/tex] is the total work done by the device
- [tex]\( Q_{\text{in}} \)[/tex] is the heat taken in by the device
Given:
- [tex]\( Q_{\text{in}} = 400 \, J \)[/tex]
- [tex]\( W_{\text{total}} = 120 \, J \)[/tex]
We can substitute these values into the formula:
[tex]\[ e = \frac{120 \, J}{400 \, J} \][/tex]
Next, calculate the efficiency [tex]\( e \)[/tex]:
[tex]\[ e = \frac{120}{400} \][/tex]
Simplify the fraction:
[tex]\[ e = 0.3 \][/tex]
Efficiency is often expressed as a percentage. To convert this to a percentage, we multiply by 100:
[tex]\[ e \times 100 = 0.3 \times 100 \][/tex]
[tex]\[ e = 30\% \][/tex]
Thus, the efficiency of the device is [tex]\( 30\% \)[/tex].
Considering the multiple-choice answers provided:
A. [tex]\( 70\% \)[/tex]
B. [tex]\( 57\% \)[/tex]
C. [tex]\( 30\% \)[/tex]
D. [tex]\( 43\% \)[/tex]
The correct answer is:
C. [tex]\( 30\% \)[/tex]
