Answer to Question #251913 in Physics for Josh

Question

A geologist working in the field drinks her morning coffee out of an aluminium cup. The cup has a mass of 0.12kg and is initially at 20°C when she pours in 0.3kg of coffee initially at 70°C.

What is the final temperature after the coffee and the cup attain thermal equilibrium? (Assume that coffee has the same specific heat capacity as water and there is no heat exchange with the surroundings.) (5 marks)

Answer 1

The heat acquired by the cup of coffee is equal to the heat lost by coffee:

$$Q_1+Q_2=0,\\ c_1m_1\Delta T_1+c_2m_2\Delta T_2=0,\\\space\\ 890·0.12(T-20)+4200·0.3(T-70)=0,\\T=66°\text{C}.$$