Question

One of the most efficient heat engines ever built is a coal-fired steam turbine in the Ohio River valley, operating between 1 870°C and 430°C.

(a) What is its maximum theoretical efficiency? %

(b) The actual efficiency of the engine is 42.0%. How much mechanical power does the engine deliver if it absorbs 1.30 105 J of energy each second from its hot reservoir?

Answer 1

(a) 68%

(b)54.6 kW

Step-by-step explanation:

(a) This would be solved by using the equation for a Carnot Engine.

e = 1 - Tc/Th

Th = the higher temperature (1870)

Tc = the lower temperature (430)

Make sure to convert to Kelvin before using these temperatures.

(b) You would use the equation for efficiency again, but using work.

e = output work/input work

In this case input work would be 1.3 x 10^5 J, and your efficiency is 42%.

0.42 = output work/(1.3 x 10^5)

output work = 54600 J

Once you have the output work, you use it to calculate power.

P = W/t

Since it is already using energy per second your answer is the same as the output work. 54600 kW