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

Answer:

The source temperature is 1248 R.

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:

$\eta_{II}=\frac{\eta_{a}}{\eta_{rev}}$

$0.6=\frac{0.35}{\eta_{rev}}$

$\eta_{rev}=0.5834$

Step2

Source temperature is calculated as follows:

$\eta_{rev}=1-\frac{T_{L}}{T}$

$\eta_{rev}=1-\frac{520}{T}$

$0.5834=1-\frac{520}{T}$

T = 1248 R.

The heat engine is shown below:

Thus, the source temperature is 1248 R.