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

Answer :

(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.

$\eta =1-\frac{T_c}{T_h}$

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

$\eta =1-\frac{300K}{800K}$

$\eta =0.625\times 100=62.5\%$

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

Formula used :

$\eta =\frac{Q_h-Q_c}{Q_h}=\frac{w}{Q_h}$

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 :

$\eta =\frac{w}{Q_h}$

$0.625=\frac{w}{1KJ}$

$w=0.625KJ$

(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.