SSC JE Mechanical Engineering 2012 Paper

Question : 118 of 200

Marks: +1, -0

A Carnot engine uses nitrogen as the working fluid. The heat supplied is 53 KJ and adiabatic expansion ratio is 16 : 1. The receiver temperature is 295 K. The heat rejected in KJ is

230
27.75
17.98
20.50

Validate

Solution:

From the Carnot theorem:

η _\Carnot=1-T_4/T_3={Q_S-Q_R}/Q_S

Now process (3-4) expansion process, expansion ratio

V_4/V_3=16:1

T_4/T_3=(V_3/V_4)^{γ-1}

⇒T_3=295/({1/16})^(0.4)=894

K
Now

η =1-295/894⇒0.67=η

0.67 ={Q_S-Q_R}/Q_S

0.67 ={53-Q_R}/53 ⇒ Q_R=17.98 \kJ

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