Question

A well-insulated styrofoam bucket contains 146 g of ice at 0 °C. If 24 g of steam at 100 °C is injected into the bucket, what is the final equilibrium temperature of the system?(cwater=4186 J/kg.°C, Lf=3.35 × 105 J/kg, Lv=2.26 × 106 J/kg). Answer in Degrees C. Please provide a detailed answer. Thank you!

Answer 1

heat lost by steam = heat gained by ice

heat = mass * specific heat * change in temperature + latent heat

heat lost by steam = change in temperature of water formed by steam + latent heat of vapourisation

heat lost by steam = 24 * 10^-3 * 4186 * (100 - T) + 24 * 10^-3 * 2.26 * 10^6

heat gained by ice = change in temperature of water formed by ice + latent heat of fusion

heat gained by the ice = 146 * 10^-3 * 4186 * (T - 0) + 146 * 10^-3 * 3.35 * 10^5

24 * 10^-3 * 4186 * (100 - T) + 24 * 10^-3 * 2.26 * 10^6 = 146 * 10^-3 * 4186 * (T - 0) + 146 * 10^-3 * 3.35 * 10^5

T = 21.6076 degree C

equilibrium temperature = 21.6076 degree C