What is the efficiency of a device that takes in [tex][tex]$400 J$[/tex][/tex] of heat and does [tex][tex]$120 J$[/tex][/tex] of work while giving off [tex][tex]$280 J$[/tex][/tex] of heat? Use [tex][tex]$e=\frac{W_{\text{total}}}{Q_{\text{in}}}$[/tex][/tex].

A. [tex]70 \%[/tex]

B. [tex]57 \%[/tex]

C. [tex]30 \%[/tex]

D. [tex]43 \%[/tex]



Answer :

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]