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?

Question

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Cricetus Cricetus · Answer 1 · 2021-04-19T08:40:23+02:00

Answer:

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

Explanation:

The given values are:

[tex]Q_1=1000 \ J[/tex]

Temperature,

[tex]T_1=900^{\circ} C[/tex]

i.e,

[tex]=1173[/tex]

[tex]T_2=5^{\circ}C[/tex]

i.e.,

[tex]=278[/tex]

As we know,

⇒ [tex]\eta =1-\frac{T_2}{T_1}[/tex]

On substituting the values, we get

⇒ [tex]=1-\frac{278}{1173}[/tex]

⇒ [tex]=\frac{1173-278}{1173}[/tex]

⇒ [tex]=\frac{895}{1173}[/tex]

⇒ [tex]=0.763[/tex]

then,

⇒ [tex]W=\eta Q_1[/tex]

⇒ [tex]=0.763\times 1000[/tex]

⇒ [tex]=763 \ J[/tex]