Question

An electric power plant manages to transfer 76% of the heat produced in the burning of fossil fuels to steam. Of the heat carried by the steam, 45 % is converted to mechanical work of the spinning turbine. Which best describes the overall efficiency of the heat-to-work conversion of the plant?

greater than 76% efficient
76% efficient
45% efficient
less than 45% efficient

Answer 1

Working backwards, the work output is

(45%) of (76%) of (the heat from the fossil fuel).

That's (0.45) x (0.76) x (the heat from the fuel)

= 0.342 of the heat from the fuel.

The overall efficiency of the heat-to-work conversion
of the plant is 34.2% .

t looks like that's less than 45% .

Answer 2

less than 45% efficient

Step-by-step explanation:

The efficiency of the heat to mechanical work conversion refers to how much of the heat is actually used to do work.

From the problem 76% of heat was converted to steam.

Let 'x' be the amount of heat from the fossil fuel/

this means out of x,
`(76)/(100)x` became steam.

which means 0.76x is steam.

It is also stated in the question that 45% of steam was used for mechanical work. which means;

`(45)/(100) * 0.76x` was converted to work.

= 0.342x

this is 34.2% of x.

Therefore the efficiency of the heat to work is less than 45%