Question

How much energy is required to take 4.5kg of -15C ice & bring it to room temperature (22C)?

Answer 1

Mass of icem=4.5kg

Initial temprature T_i=-15 C

Final temprature T_f= 22 C

First the energy is E₁ reqiured to take ice from -15C to 0 C

Then Energy  E₂ reqiure to convert ice to water at 0 C.

Then Energy E₃ reqiure to rise the tempraure of water from 0 C to 22 C.

For E₁ the temperature of the ice changes from -15C to 0 C

The amount of heat is given by Q=mC(T_f -T_i) ,where C is specific heat of ice c=2090 J/Kg C

E₁=4.5 2090 (0-(-15)) = 4.5 209015 =141,075 J

When the temperature of the ice reaches 0.0°C, the ice –water mixture
remains at this temperature . So Energy E₂ require to melt it .

E₂ =mL, where L is latent heat of melting

E₂ = 4.53.310⁵ = 14.85 10⁵ J

The amount of energy necessary to increase the temperature from 0.0°C to 22 C

E₃= mc_w(T_f - T_i ), where c_w is specific heat of water , c_w=4.19 10³ J/kg.C

E₃=4.5 4.19 10³(22-0) = 4.5 4.19 10³22 = 414.81 10³ J

Total Energy E = E₁ + E₂ + E₃ =141,075 + 414.81 10³  + 14.85 10⁵ = 2.040885 10⁶ J = 2.04 10⁶ J