Answer :
To find the engine's efficiency, we use the formula for efficiency in thermodynamics, which is defined as the ratio of the net work output to the heat input:
[tex]\[ \text{Efficiency} = \frac{\text{Work Done}}{\text{Heat Added}} \][/tex]
Given:
- Heat added to the engine, [tex]\( Q_{\text{added}} = 2.5 \times 10^4 \, \text{J} \)[/tex]
- Net work done by the engine, [tex]\( W_{\text{done}} = 7.0 \times 10^3 \, \text{J} \)[/tex]
Now, plug these values into the efficiency formula:
[tex]\[ \text{Efficiency} = \frac{W_{\text{done}}}{Q_{\text{added}}} = \frac{7.0 \times 10^3 \, \text{J}}{2.5 \times 10^4 \, \text{J}} \][/tex]
Performing the division to find the efficiency:
[tex]\[ \frac{7.0 \times 10^3}{2.5 \times 10^4} = 0.28 \][/tex]
Thus, the efficiency of the engine is [tex]\(0.28\)[/tex], which is the decimal form of the efficiency.
If we need to express the efficiency as a percentage, we multiply the decimal form by 100:
[tex]\[ \text{Efficiency Percentage} = 0.28 \times 100 = 28.00\% \][/tex]
Therefore, the correct answer to the question is:
C. 0.28
[tex]\[ \text{Efficiency} = \frac{\text{Work Done}}{\text{Heat Added}} \][/tex]
Given:
- Heat added to the engine, [tex]\( Q_{\text{added}} = 2.5 \times 10^4 \, \text{J} \)[/tex]
- Net work done by the engine, [tex]\( W_{\text{done}} = 7.0 \times 10^3 \, \text{J} \)[/tex]
Now, plug these values into the efficiency formula:
[tex]\[ \text{Efficiency} = \frac{W_{\text{done}}}{Q_{\text{added}}} = \frac{7.0 \times 10^3 \, \text{J}}{2.5 \times 10^4 \, \text{J}} \][/tex]
Performing the division to find the efficiency:
[tex]\[ \frac{7.0 \times 10^3}{2.5 \times 10^4} = 0.28 \][/tex]
Thus, the efficiency of the engine is [tex]\(0.28\)[/tex], which is the decimal form of the efficiency.
If we need to express the efficiency as a percentage, we multiply the decimal form by 100:
[tex]\[ \text{Efficiency Percentage} = 0.28 \times 100 = 28.00\% \][/tex]
Therefore, the correct answer to the question is:
C. 0.28
