Respuesta :
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 [tex]T_h[/tex] = 800 K
Temperature of cold body [tex]T_c[/tex] = 300 K
(a) First we have to calculate the maximum efficiency of the engine.
Formula used for efficiency of the engine.
[tex]\eta =1-\frac{T_c}{T_h}[/tex]
Now put all the given values in this formula, we get :
[tex]\eta =1-\frac{300K}{800K}[/tex]
[tex]\eta =0.625\times 100=62.5\%[/tex]
(b) Now we have to calculate the maximum work done.
Formula used :
[tex]\eta =\frac{Q_h-Q_c}{Q_h}=\frac{w}{Q_h}[/tex]
where,
[tex]Q_h[/tex] = heat supplied by hot source = 1 KJ
[tex]Q_c[/tex] = heat supplied by hot source
w = work done = ?
Now put all the given values in this formula, we get :
[tex]\eta =\frac{w}{Q_h}[/tex]
[tex]0.625=\frac{w}{1KJ}[/tex]
[tex]w=0.625KJ[/tex]
(c) Now we have to calculate the heat discharge into the cold sink.
Formula used :
[tex]w=Q_h-Q_c[/tex]
[tex]Q_c=Q_h-w[/tex]
[tex]Q_c=1-0.625[/tex]
[tex]Q_c=0.375KJ[/tex]
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.
