Example of heat and thermodynamics | Learn Physics

Example of heat and thermodynamics

Example: Ice in a cold storage melts at a rate of 2.5 kg/hour. When the external temperature is 27˚ C. Find the minimum power output of the motor of the refrigerator which just prevents the ice from melting. Latent heat of fusion of ice = 80 cal/g.

Solution:  To prevent melting of ice, heat energy is to be taken out.

Heat energy to be removed/hour     mL = 2.5 × 10³ ×80 cal/hour

Heat energy to be removed/sec       Q₂ =( 2.5 × 10³ × 80 )/( 60  ×  60) =55.55 cal/s

                                                                          = 55.55 × 4.2 J/s =233.3 J/s

As     T₁ = 27˚ C = 27 + 273 = 300 K

And   T₂  = 0˚ C = 0+ 273 = 273 K

Coefficient of performance,   β = T₂ / (T₁ – T₂)=273/(300-273)=273/27

As                β = Q₂ /W

                         W   = Q₂ / β = 233.3/(273/27)= 27  × 233.3/273

                        W = 6300.0

273= 23.1 watt

This is the minimum power output of the motor