Final answer:
The heat capacity of the coffee cup calorimeter is calculated by using the formula q = m · c · ΔT with the principle of conservation of energy and accounting for heat lost by warm water and gained by cooler water.
Step-by-step explanation:
To find the heat capacity of the coffee cup calorimeter, we can use the concept of conservation of energy, which implies that heat lost by the warm water will be gained by the cooler water and the calorimeter.
Since the specific heat of water is given as 4.184 J/g°C, we can calculate the heat exchanged using the formula
q = m · c · ΔT,
where q is the heat exchange,
m is the mass,
c is the specific heat capacity,
and ΔT is the change in temperature.
Both water samples have the same mass, and thus each will lose/gain the same amount of heat to reach the final temperature.
Therefore, we calculate the heat change for the warm water: q₁ = m · c · (ΔT) = 25.0 g · 4.184 J/g°C · (29.5°C - 40.0°C).
Since warm water is cooling down, the ΔT will be negative, indicating heat is lost.
Likewise, the cooler water's heat change is q₂ = m · c · (ΔT) = 25.0 g ·
4.184 J/g°C · (29.5°C - 20.0°C).
A positive ΔT indicates heat is gained. The calorimeter gains the remaining heat.
Assuming no heat loss to the surroundings, q₁ + q₂ + q₃(calorimeter) = 0. Solving for q₃(calorimeter) gives us the heat capacity of the coffee cup calorimeter, which can be calculated and matched to the options provided.