Question

The maximum possible efficiency of a reversible heat engine is 79.46% when the cold temperature is 224.0°C. What is the hot temperature in degrees Celsius?

Answer 1

We have

A heat engine is 79.46%

TC= 224.0°C

TH=?

we have the next formula

`\eta(\text{\%)}=1-(T_C)/(T_H)*100`

we substitute the values

`.7946=1-(224)/(T_H)*100`

then we isolate TH

`\begin{gathered} .07946-1=-(T_C)/(T_H)*1 \\ -0.2054=-(T_C)/(T_H)*1 \\ (T_C)/(T_H)*1=-0.2054 \\ (T_C)/(T_H)=(0.2054)/(1) \\ (T_H)/(T_C)=(1)/(0.2054) \\ T_H=4.8685\cdot224 \\ T_H=1090.55\text{ \degree{}C} \end{gathered}`

the hot temperature is 1090.55 degrees Celsius.