Question

A certain heat engine operates between 800 K and 300 K. (a) What is the maximum efficiency of the engine? (b) Calculate the maximum work that can be done by for each 1.0 k) of hea a reversible process for each 1.0 kJ supplied by the hot source? t supplied by the hot source. (c) How much heat is discharged into the cold sink in

Answer 1

(a) The maximum efficiency of the engine is, 62.5 %

(b) The maximum work done is, 0.625 KJ.

(c) The heat discharge into the cold sink is, 0.375 KJ.

Explanation : Given,

Temperature of hot body
`T_h` = 800 K

Temperature of cold body
`T_c` = 300 K

(a) First we have to calculate the maximum efficiency of the engine.

Formula used for efficiency of the engine.

`\eta =1-(T_c)/(T_h)`

Now put all the given values in this formula, we get :

`\eta =1-(300K)/(800K)`

`\eta =0.625* 100=62.5\%`

(b) Now we have to calculate the maximum work done.

Formula used :

`\eta =(Q_h-Q_c)/(Q_h)=(w)/(Q_h)`

where,

`Q_h` = heat supplied by hot source = 1 KJ

`Q_c` = heat supplied by hot source

w = work done = ?

Now put all the given values in this formula, we get :

`\eta =(w)/(Q_h)`

`0.625=(w)/(1KJ)`

`w=0.625KJ`

(c) Now we have to calculate the heat discharge into the cold sink.

Formula used :

`w=Q_h-Q_c`

`Q_c=Q_h-w`

`Q_c=1-0.625`

`Q_c=0.375KJ`

Therefore, (a) The maximum efficiency of the engine is, 62.5 %

(b) The maximum work done is, 0.625 KJ.

(c) The heat discharge into the cold sink is, 0.375 KJ.