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

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

Step-by-step 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-(T_2)/(T_1)`

On substituting the values, we get

⇒
`=1-(278)/(1173)`

⇒
`=(1173-278)/(1173)`

⇒
`=(895)/(1173)`

⇒
`=0.763`

then,

⇒
`W=\eta Q_1`

⇒
`=0.763* 1000`

⇒
`=763 \ J`