Question

A mass of 15 kg of air in a piston–cylinder device is heated from 25 to 77°C by passing current through a
resistance heater inside the cylinder. The pressure inside the cylinder is maintained constant at 300 kPa during
the process, and a heat loss of 60 kJ occurs. Determine the electric energy supplied, in kWh.

Answer 1

Answer:

The electrical energy supplied is 0.233 kWh

Explanation:

Given :

Mass of air kg

Initial temperature 298 K

Final temperature 350 K

Heat loss kJ

From the first law of thermodynamics,

   

We know that internal energy is proportional to difference of temperature,

 

 

Now we need answer into kWh so ( 1 kWh = 3600 kJ ).

So we need to multiply ( )

     kWh

     kWh

Therefore, the electrical energy supplied 0.233 kWh

Answer 2

Given = mass of air 15 kg

           $T_{1} =$ 25°

           $T_{2} =$ 77°

          $P_{1} = P_{2}$

          = 300 $kPa$

          $Q_{2} =$ -60 $k j$ (negative sign for loss of heat )

by first law of thermodynamic

       $Q_{2} - W_{2}$ = $m (u_{2} -u_{1} )$

       P = ($V_{2} - V_{1}$)

Assume heat constant

   $h_{2}-h_{1}$ = $C_{p}$ $(T_{2}-T_{1})$

           $T_{1} =$ 25° + 273 = $298^{k}$

           $T_{2} =$ 77° + 273 = $350^{k}$

=   (-60)-(15) x (1.005-$\frac{kg}{KI}$) (350-298k)

=  0.2344 kwh

hence the electric energy is supplied is 0.2344 kWh