A woman working in the field drinks her morning coffee out of an aluminium cup. The cup has a mass of 0.120 kg and is initially at `20.0^(@)C` when she pours in 0.300 kg of coffee initially at `70.0^(@)C`. What is te final temperature after the coffee and the cup attain thermal equilibrium? (Assume that coffee has the same specific heat as water and that there is no heat exchange with the surroundings).

Explanation

To solve the problem of finding the final temperature after the coffee and the aluminum cup attain thermal equilibrium, we can follow these steps:

### Step 1: Identify the known values
- Mass of the aluminum cup, \( m_{cup} = 0.120 \, \text{kg} \)
- Initial temperature of the cup, \( T_{cup, initial} = 20.0 \, ^\circ C \)
- Mass of the coffee, \( m_{coffee} = 0.300 \, \text{kg} \)
- Initial temperature of the coffee, \( T_{coffee, initial} = 70.0 \, ^\circ C \)
- Specific heat capacity of water (and coffee), \( c_{water} = 4200 \, \text{J/(kg} \cdot ^\circ C) \)
...