Question

Hot water of mass 300g and at a temperature of 90°C is added to 200g of cold water at 10°C. What is the final temperature of the mixture?

a) 32.5°C
b) 45.0°C
c) 50.0°C
d) 60.0°C

Answer 1

To determine the final temperature of a mixture of hot and cold water, we use the conservation of energy principle. By equating the heat lost by the hot water to the heat gained by the cold water and solving for the final temperature, we find that the correct answer is d) 60°C.

Step-by-step explanation:

To find the final temperature of the mixture, we can use the principle of conservation of energy, which states that the heat lost by the hot water will be equal to the heat gained by the cold water, assuming no heat is lost to the surroundings. We have 300g of hot water at 90°C and 200g of cold water at 10°C.

The specific heat capacity of water is 4.18 J/g°C. Using the formula:

Q = mcΔT (where Q is the heat exchanged, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature), we can set the heat gained by the cold water equal to the heat lost by the hot water:

1. Let T represent the final temperature.
2. The heat lost by hot water is: Qhot = (300g)(4.18 J/g°C)(90°C - T).
3. The heat gained by cold water is: Qcold = (200g)(4.18 J/g°C)(T - 10°C).
4. Set Qhot equal to Qcold and solve for T:
5. (300g)(4.18 J/g°C)(90°C - T) = (200g)(4.18 J/g°C)(T - 10°C)
6. Simplify and solve the equation for T.
7. The final temperature T can be calculated to be 60°C.

Therefore, the correct answer is d) 60°C.