Final answer:
It takes approximately 93,255.872 joules to heat a 313 mL cup of Starbucks coffee from a room temperature of 23°C to 94.6°C, using the specific heat capacity of water and the formula Q = mcΔT.
Step-by-step explanation:
To calculate how much heat energy in joules it takes to raise the temperature of a 313 mL cup of Starbucks coffee (mostly water) from room temperature (23°C) to 94.6°C, we use the formula Q = mcΔT, where:
- Q is the heat energy in joules,
- m is the mass of the coffee in kilograms,
- c is the specific heat capacity of water (approximately 4.184 J/g°C),
- ΔT is the change in temperature in degrees Celsius.
First, convert 313 mL of water to grams (since the density of water is 1 g/mL, 313 mL of water is equivalent to 313 g). Then convert grams to kilograms by dividing by 1000, which gives us 0.313 kg.
The change in temperature (ΔT) is 94.6°C - 23°C = 71.6°C.
Next, plug these values into the formula:
Q = (0.313 kg)(4.184 J/g°C)(71.6°C)
Q = 0.313 kg * 4.184 J/g°C * 71.6°C * 1000 g/kg
Q = 93,255.872 J
Therefore, it takes approximately 93,255.872 joules to raise the temperature of a 313 mL cup of Starbucks coffee from 23°C to 94.6°C.