Question

An insulated thermos contains 106 cm3 of hot coffee at a temperature of 67.0◦C. You put in 12.0 g of ice at its melting point to cool the coffee. By how many degrees has your coffee cooled just after all the ice has melted and equilibrium is reached? Treat the coffee as though it were pure water and neglect energy exchanges with the environment.

Answer 1

= density of coffee = 1 g/cm³

V = Volume = 106 cm³

mass of coffee is given as

M = V = 1 x 106 = 106 g = 0.106 kg

T_ic = initial temperature of coffee = 67 C

T_ii = initial temperature of ice = 0 C

T = final equilibrium temperature = ?

c = specific heat of water = 4186

m = mass of ice added = 12 g = 0.012 kg

L = latent heat of fusion of ice to water = 334 x 10³ J/kg

using conservation of heat

heat gained by ice = Heat lost by Coffee

m L + m c (T - T_ii) = M c (T_ci - T)

(0.012) (334 x 10³) + (0.012) (4186) (T - 0) = (0.106) (4186) (67 - T)

T = 52.1 C