Final answer:
To find the approximate temperature of Jose's hot chocolate after adding cold milk, we can use the principles of conservation of energy and the specific heat capacities of the hot chocolate and milk. We can set up an equation using the heat lost by the hot chocolate and the heat gained by the milk. Solving this equation will give us the final temperature of the hot chocolate.
Step-by-step explanation:
To find the approximate temperature of Jose's hot chocolate after adding cold milk, we can use the principle of conservation of energy. The heat lost by the hot chocolate is equal to the heat gained by the cold milk. The heat lost by the hot chocolate can be calculated using Q = mcΔT, where Q is the heat, m is the mass, c is the specific heat, and ΔT is the change in temperature.
Given that the hot chocolate initially had a temperature of 95°C and a volume of 200 mL, we can use the density of water (1 g/mL) to find the mass of the hot chocolate, which is 200 g. The specific heat of hot chocolate can be assumed to be similar to that of water (4.18 J/g°C). The heat lost by the hot chocolate is then 200 g × 4.18 J/g°C × (95°C - T), where T is the final temperature.
The heat gained by the cold milk can be calculated in a similar manner. Given that the milk initially had a temperature of 5°C and a volume of 50 mL, we can find its mass using the density of water (1 g/mL), which is 50 g. Assuming the specific heat of milk is similar to that of water (4.18 J/g°C), the heat gained by the milk is 50 g × 4.18 J/g°C × (T - 5°C).
Since the heat lost by the hot chocolate is equal to the heat gained by the milk, we can set up the equation: 200 g × 4.18 J/g°C × (95°C - T) = 50 g × 4.18 J/g°C × (T - 5°C). Solving this equation will give us the final temperature of the hot chocolate.