Answer:
The final temperature of the bath water will be 55°C
Explanation:
A student is preparing to take a bath when she realizes that the hot water tap is not working.
The student goes to the kitchen and prepares 10 L of 100 degree Celsius water to mix with 10 L of 10 degree Celsius water. What will be the final temperature of the bath water?
Using the relation, Heat lost = Heat gained (assuming no heat is lost to the surroundings).
Heat lost by hot water = heat gained by cold water
Using the formula of heat, Q = mcΔT
where m = mass of water, c = specific heat capacity of water, ΔT = temperature difference
mass of water = density * volume (density of water = 1 kg/L)
mass of hot water, m₁ = 1 kg/L * 10 L = 10 kg;
mass of cold water, m₂ = 1 kg/L * 10 L = 10 kg;
specific heat capacity of water, c = 4200 j/kg
Let the final temperature of the mixture be T
-m₁cΔT₁ = m₂cΔT₂ ( since heat is lost by the hot water)
-m₁ΔT₁ = m₂ΔT₂
-10 * (T- 100) = 10 * (T - 10)
-10T + 1000 = 10T - 100
20T = 1100
T = 1100/20
T = 55°C
Therefore, the final temperature of the bath water will be 55°C
