Total heat required = heat required to raise 8kg of ice from - 16 degrees to 0 degrees + heat required to melt 8kg of ice + heat required to raise the temperature of 8kg of water from 0 degrees to 30 degrees
The formula for calculating the heat required to raise the temperature is expressed as
H = mcθ
where
m is the mass of the substance
c is the specific heat capacity of the ice
θ is the change in temperature
From the information given,
m = 8kg = 8 x 1000 = 8000g
c = 2.09 J/g^-1K-^-1
θ = 0 - - 16 = 16
heat required to raise 8kg of ice from - 16 degrees to 0 degrees = 8000 x 2.09 x 16 = 267520J
The formula for calculating latent heat of fusion is
H = ml
where
l is the latent heat of fusion of ice = 334 J/g
heat required to melt 8kg of ice = 8000 x 334 = 2672000 J
heat required to raise the temperature of 8kg of water from 0 degrees to 30 degrees
= 8000 x 4.184 x (30 - 0) = 1004160 J
Total heat required = 267520 + 2672000 + 1004160
Total heat required =