the chart shows data for four heat engines.\n| heat engine | $t_{h}(k)$ | $t_{c}(k)$ |\n| ---- | ---- |…

the chart shows data for four heat engines.\n| heat engine | $t_{h}(k)$ | $t_{c}(k)$ |\n| ---- | ---- | ---- |\n| w | 620 | 120 |\n| x | 840 | 100 |\n| y | 900 | 300 |\n| z | 500 | 25 |\nwhich lists the engines from most efficient to least efficient?\no y, x, w, z\no z, w, x, y\no z, x, w, y\no y, w, x, z

the chart shows data for four heat engines.\n| heat engine | $t_{h}(k)$ | $t_{c}(k)$ |\n| ---- | ---- | ---- |\n| w | 620 | 120 |\n| x | 840 | 100 |\n| y | 900 | 300 |\n| z | 500 | 25 |\nwhich lists the engines from most efficient to least efficient?\no y, x, w, z\no z, w, x, y\no z, x, w, y\no y, w, x, z

Answer

Explanation:

Step1: Recall efficiency formula

The efficiency formula for a heat - engine is $\eta = 1-\frac{T_c}{T_h}$, 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 $\eta_W=1 - \frac{120}{620}=1-\frac{6}{31}=\frac{31 - 6}{31}=\frac{25}{31}\approx0.806$.

Step3: Calculate efficiency of engine X

For engine X, $T_h = 840$ K and $T_c = 100$ K. Then $\eta_X=1-\frac{100}{840}=1-\frac{5}{42}=\frac{42 - 5}{42}=\frac{37}{42}\approx0.881$.

Step4: Calculate efficiency of engine Y

For engine Y, $T_h = 900$ K and $T_c = 300$ K. Then $\eta_Y=1-\frac{300}{900}=1-\frac{1}{3}=\frac{2}{3}\approx0.667$.

Step5: Calculate efficiency of engine Z

For engine Z, $T_h = 500$ K and $T_c = 25$ K. Then $\eta_Z=1-\frac{25}{500}=1-\frac{1}{20}=\frac{19}{20}=0.95$.

Step6: Compare efficiencies

Comparing the values: $\eta_Z = 0.95$, $\eta_X\approx0.881$, $\eta_W\approx0.806$, $\eta_Y\approx0.667$.

Answer:

Z, X, W, Y