Question

An engine draws energy from a hot reservoir with a temperature of 1250 K and exhausts energy into a cold reservoir with a temperature of 322 K. Over the course of one hour, the engine absorbs 1.37 x 105 J from the hot reservoir and exhausts 7.4 x 104 J into the cold reservoir.
1) What is the power output of this engine?

2) What is the maximum (Carnot) efficiency of a heat engine running between these two reservoirs?

3) What is the actual efficiency of this engine?

Answer 1

Answer:

The power output of this engine is  $P = 17.5 W$

The  the maximum (Carnot) efficiency is  $\eta_c = 0.7424$

The  actual efficiency of this engine is  $\eta _a = 0.46$

Explanation:

From the question we are told that

    The temperature of the hot reservoir is  $T_h = 1250 \ K$

      The temperature of the cold reservoir  is  $T_c = 322 \ K$

     The energy absorbed from the hot reservoir is $E_h = 1.37 *10^{5} \ J$

       The energy exhausts into  cold reservoir is  $E_c = 7.4 *10^{4} J$

The power output is mathematically represented as

      $P = \frac{W}{t}$

Where t is the time taken which we will assume to be 1 hour =  3600 s  

W is the workdone which is mathematically represented as

      $W = E_h -E_c$

substituting values

       $W = 63000 J$

So

    $P = \frac{63000}{3600}$

    $P = 17.5 W$

The Carnot efficiency is mathematically represented as

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

         $\eta_c = 1 - \frac{322}{1250}$

         $\eta_c = 0.7424$

The actual efficiency is mathematically represented as

        $\eta _a = \frac{W}{E_h}$

substituting values

         $\eta _a = \frac{63000}{1.37*10^{5}}$

         $\eta _a = 0.46$