Question

A power plant burns coal to generate electricity. Suppose that 1000 J of heat (Q) from the coal fire enters a boiler, which is kept at a constant temperature of 900 C. That 1000 J is used to boil water in a boiler. The steam from the boiler is used to drive a turbine that creates electricity (work). The excess heat is put into a cooling tower at 5 C.
Carnot efficiency If everything is perfectly efficient,
• What is the maximum efficiency that the plant could operate at?
• How much work could be done starting from that 1000 J?

Answer 1

Answer:

The work done will be "763 J". A further explanation is given below.

Explanation:

The given values are:

$Q_1=1000 \ J$

Temperature,

$T_1=900^{\circ} C$

i.e,

    $=1173$

$T_2=5^{\circ}C$

i.e.,

    $=278$

As we know,

⇒  $\eta =1-\frac{T_2}{T_1}$

On substituting the values, we get

⇒     $=1-\frac{278}{1173}$

⇒     $=\frac{1173-278}{1173}$

⇒     $=\frac{895}{1173}$

⇒     $=0.763$

then,

⇒  $W=\eta Q_1$

⇒       $=0.763\times 1000$

⇒       $=763 \ J$