Mechanical Engineering Mathematical Exam Questions (Air Refrigeration Cycles, Q-2)

➢➣An ice plant produces 100 tons of ice in 24 hrs. If the plant uses water at 20⁰ C, find its cooling capacity. Specific heat and latent heat of solidification of water are 4.2 kJ/kg/K and 334 kJ/kg respectively. 

Solution:

Given,

           m = 100 tons = 100000 Kg

           T = 20⁰C = 293 K

           Specific heat, c_f = 4.2 kJ/kg/K

           Latent heat of solidification, h_fg = 334 kJ/kg

           Cooling Capacity =?

We know that,

                Heat removed from water to ice at 20⁰C,

                                      Q₁ = m c_f T 

                                           = 100000 x 4.2 x 293

                                           =1.23 x10⁸ KJ

                Total latent heat of freezing,

                                      Q₂ = m h_fg 

                                           = 100000 x 334 

                                           = 3.34 x10⁷ KJ

                Total heat removed in 24 hours,

                                      Q = Q₁ + Q₂  

                                          = 1.23 x10⁸+3.34 x10⁷ 

                                                        = 156.46 x10⁶ KJ

                So, Heat removed in 1 minutes 

                                         = 156.46 x10⁶/(24 x 60)

                                         = 108.62 x10³ KJ/min

                Cooling Capacity, 

                                        = 108.62 x10³/210 

                                        = 517.39 TR

So, Cooling Capacity of ice plant is = 517.39 TR