Question

As an eager scientist on a hot summer day you wish to determine how much ice to buy to add to your cooler which is filled with 32 cans of soda which are warm at 87.7°F. Each can has a mass of 420 g and ideally you want the temperature of the drinks to be 40.8°F. If there is no heat lost by the cooler and ignoring any heat lost to the soda containers, how much ice needs to be added to your cooler? (Assume the temperature of the ice is 32.0°F.)

Answer 1

Sol:

Given data

• n = 32 sodas
• mass (m) = 420 g = 0.42 kg
• Total mass of the soda is (M)

• 

convert Fto ⁰C

Convert ⁰C to K

• Temperature to which the soda has to be cooled is

• Temperature of the ice is

• Mass of the ice needed to cooler the soda is

formula is

where T₁ = Initial temperature

T₂ = temperature of the soda has to be cooled

M = total mass

m_ice = mass of ice required to cool the soda

L_f= latent heat of fusion of ice is 3.33*10⁵ j/kg

C = Heat capacity of water is 4186 J / kg K

Mass of the material used for making the soda cans are small. So so it is negligible then (M) we consider the total mass(M). Specific heat capacity of soda(C) is equal to that of water.To melt the ice it needs heat energy, this energy will be taken from the soda present in the cooler..So heat energy lost by the soda will be equal to the heat energy utilized for melting of the ice.