What is the mass of the cup

Question

A 80 gram ice cube at -10 degree's celsius is placed in an aluminum cup whose initial temperature is 70 degree's celsius . The system comes to an equilibrium temperature of 20 degree celsius.

What is the mass of the cup? in kg

Express your answer using two significant figures.

Answer 1

Heating the Ice from -10°C to 0°C = 80g x 2.05J/g/°C x 10°C.

= 1,640J.

Heat required to melt the ice = 80g x 334J/g.

= 26,720J.

Heating the water from 0°C to 20°C.

= 80g x 4.184J/g/°C x 20°C ΔT.

= 6,694J.

Heat gained by ice = 1,640 + 26,720 + 6.694 = 35kJ.

Heat Lost by the cup = Mass (kg) x 0.9kJ/kg/°C x 50°C ΔT.

= g x 45kJ

Mass (g) = 35kJ / 45kJ = 0.78kg