Question

A heat engine that rejects waste heat to a sink at 520 R has a thermal efficiency of 35 percent and a second- law efficiency of 60 percent. Determine the temperature of the source that supplies heat to this engine.

Answer 1

The source temperature is 1248 R.

Step-by-step explanation:

Second law efficiency of the engine is the ratio of actual efficiency to the maximum possible efficiency that is reversible efficiency.

Given:

Temperature of the heat sink is 520 R.

Second law efficiency is 60%.

Actual thermal efficiency is 35%.

Calculation:

Step1

Reversible efficiency is calculated as follows:

`\eta_(II)=(\eta_(a))/(\eta_(rev))`

`0.6=(0.35)/(\eta_(rev))`

`\eta_(rev)=0.5834`

Step2

Source temperature is calculated as follows:

`\eta_(rev)=1-(T_(L))/(T)`

`\eta_(rev)=1-(520)/(T)`

`0.5834=1-(520)/(T)`

T = 1248 R.

The heat engine is shown below:

Thus, the source temperature is 1248 R.