Respuesta :
Answer:
- The amount of milk in ml you must add to reach 70.00ºC is 56.2 ml.
Explanation:
1. Change of temperature of the milk.
Milk will heat up from 1.00°C. Naming Qm the heat absorbed by milk, Mm the mass of milk added, in grams, and C the specific heat:
- Qm = Mm × C × (70.00°C - 1.00°C)
2. Change of temperature of the coffe.
Coffe will cooldown from 90.0°C. Naming Qc the heat released by coffe, Mc the mass of coffe, in grams, and C the specific heat:
- Qc = Mc × C × (90.0°C - 70.0°C)
3. Final mixture
The amount of coffe at 90.0°C plus the amount of milk at 1.00°C is 250 ml
Since the density is assumed to be 1.000g/ml, the mass is 250 g.
- Mm = 250 g - Mc
4. Assumptions:
- C = 4.184 J/gºC, for both milk and coffee
- Qm = Qc, because the coffee in in an insulated travel mug.
5. Calculations:
- Qm = Qc
- Mm × C × (70.00°C - 1.00°C) = (250g - Mm) × C × (90.0°C - 70.0°C)
- Mm × 69.00 = (250 - Mm) × 20.00
- 69Mm = 5,000 - 20Mm
- Mm = 5,000 / (89)
- Mm = 56.2 g
Since the density is 1.000g/mol, 56.2g is 56.2 ml
Answer: 56.2 ml