In a hypothetical nuclear fusion reactor, the fuel is deuterium gas at a temperature of about 9.5 x 108 K. If this gas could be used to operate a Carnot engine with TL = 864°C, what would be the engine's efficiency?

Respuesta :

Answer:

Engine's Efficiency = 99.9998%

Explanation:

Given :

The temperature of the gas is , TH = 9.5 *10⁸ K

The operation temperature of the gas is , TL = 864 °C

The conversion of T( °C) to T(K) is shown below:

T(K) = T( °C) + 273.15  

So,  

TL = (864 + 273.15) K = 1137.15 K  

The engine's efficiency of a Carnot engine is:

[tex]Carnot's\ Efficiency=\frac {T_H-T_L}{T_H}\times 100 \%[/tex]

So,

[tex]Carnot's\ Efficiency=\frac {(9.5\times 10^8)-1137.15}{9.5\times 10^8}\times 100 \%[/tex]

Engine's Efficiency = 99.9998%

                                     

Answer:99.99 %

Explanation:

Given

Temperature of deuterium gas[tex]\left ( T_H\right ) =9.5\times 10^8 k[/tex]

Lower temperature[tex]\left ( T_L\right )=864^{\circ}C\approx 1137 k[/tex]

We know that Engine efficiency [tex]\left ( \eta \right )[/tex] is given by

[tex]\eta =\frac{Work ouput}{heat supplied} [/tex]

and carnot efficiency[tex]\left ( \eta \right )=1-\frac{T_L}{T_H}-----------\left ( Maximum\ efficiency\right ) [/tex]

[tex]\eta =1-\frac{1173}{9.5\times 10^8}[/tex]

[tex]\eta =0.9999[/tex]

99.99%