Question

the chart shows data for four heat engines. heat engine tₕ (k) tₑ (k) w 620 120 x 840 100 y 900 300 z 500 25 which lists the engines from most efficient to least efficient? y, x, w, z z, w, x, y z, x, w, y y, w, x, z

Explanation:

Step1: Recall efficiency formula

The efficiency of a heat - engine is given by $\eta = 1-\frac{T_{c}}{T_{h}}$, where $T_{h}$ is the high - temperature reservoir and $T_{c}$ is the low - temperature reservoir.

Step2: Calculate efficiency of engine W

For engine W, $T_{h}=620$ K and $T_{c}=120$ K. Then $\eta_{W}=1 - \frac{120}{620}=\frac{620 - 120}{620}=\frac{500}{620}\approx0.806$.

Step3: Calculate efficiency of engine X

For engine X, $T_{h}=840$ K and $T_{c}=100$ K. Then $\eta_{X}=1-\frac{100}{840}=\frac{840 - 100}{840}=\frac{740}{840}\approx0.881$.

Step4: Calculate efficiency of engine Y

For engine Y, $T_{h}=900$ K and $T_{c}=300$ K. Then $\eta_{Y}=1-\frac{300}{900}=\frac{900 - 300}{900}=\frac{600}{900}\approx0.667$.

Step5: Calculate efficiency of engine Z

For engine Z, $T_{h}=500$ K and $T_{c}=25$ K. Then $\eta_{Z}=1-\frac{25}{500}=\frac{500 - 25}{500}=\frac{475}{500}=0.95$.

Step6: Rank the engines

Comparing the efficiencies: $\eta_{Z}>\eta_{W}>\eta_{X}>\eta_{Y}$. So the order from most efficient to least efficient is Z, W, X, Y.

Answer:

Z, W, X, Y