Question

A power plant burns coal at
830 K, and exhausts to air at
288 K. If it runs at the Carnot
efficiency, how much input heat
must be fed into the plant to
produce 230,000 J of work?
(Unit = J)

Answer 1

The amount of heat fed to the plant is 353846.15J

Efficiency of engine:

The efficiency of an engine is defined as ratio of the useful work done to the heat provided or,

in terms of temperature of the source and the sink the efficiency of heat engine is given by $1-\frac{T_{2} }{T_{1} }$

Thus, we have two formulae to calculate the efficiency of a heat engine.

η= $\frac{useful work done}{heat absorbed}$ ....1

η= $1-\frac{T_2}{T_1}$             ....2   (where $T_{2}$ and $T_{1}$ are temperatures of sink and source respectively)

Given quantities are,

• $T_{1}$ = 830K

• $T_1$ =288K

• Work done = 230000J

Now, by equating (1) and (2) equation,

⇒ $1-\frac{T_2}{T_1}$ = $\frac{Useful work done}{Heat absorbed}$

Substituting the given values;

⇒ $1-\frac{288}{830}$ = $\frac{230000}{heat absorbed}$

⇒therefore, heat absorbed = 353846.15 J

To learn more about efficiency of heat engine, referhttps://brainly.com/question/13155544

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