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

Answer:

less than 45% efficient

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, $\frac{76}{100}x$ 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;

$\frac{45}{100} * 0.76x$ was converted to work.

= 0.342x

this is 34.2% of x.

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