Question

Two engines A and B have their sources at 400K and 350K and sinks at 350K and 300K respectively. Which is more efficient and by how much?

Answer 1

Answer:

2 engines A and B such that:

For Engine A :

• Source Temperature = 400K
• Sink Temperature = 350 K

For Engine B:

• Source temperature = 350 K
• Sink Temperature = 300 K

To Find:

Which engine I more efficient and by how much ?

Calculation :

For Engine A :

$\eta = 1 - \frac{sink \: temp.}{source \: temp.}$

$= > \eta = 1 - \frac{350}{400}$

$= > \eta = 1 - \frac{7}{8}$

$= > \eta = \frac{1}{8}$

$= > \eta = 0.125$

For Engine B:

$\eta = 1 - \frac{sink \: temp.}{source \: temp.}$

$= > \eta = 1 - \frac{300}{350}$

$= > \eta = 1 - \frac{6}{7}$

$= > \eta = \frac{1}{7}$

$= > \eta = 0.142$

So Engine B is more efficient than

Engine A.

Efficiency of Engine B is more than Engine A by (0.142 - 0.125) = 0.017

So final answer is :

$\boxed{ \red{diff. \: in \: (\eta) = 0.01785}}$