Hot water of mass 80g, at a temperature of 100degree celcius is pourd into 30g of water at 30degree celcius. Assuming that no heat is lost, calculate the final temperature
To calculate the final temperature after mixing the hot water and cold water, we can use the principle of conservation of energy, specifically the principle of thermal equilibrium.
The principle of thermal equilibrium states that when two objects at different temperatures are brought into contact with each other, heat will flow from the object with higher temperature to the object with lower temperature until both objects reach the same final temperature.
To calculate the final temperature, we can use the formula:
(m1 * c1 * ΔT1) + (m2 * c2 * ΔT2) = 0
Where:
m1 and m2 are the masses of the hot water and cold water respectively,
c1 and c2 are the specific heat capacities of water (4.184 J/g°C),
ΔT1 is the change in temperature of the hot water (final temperature - initial temperature of hot water),
ΔT2 is the change in temperature of the cold water (final temperature -initial temperature of cold water),
and 0 indicates that no heat is lost.
Let's plug in the values into the formula:
(80g * 4.184 J/g°C * (final temperature - 100°C)) + (30g * 4.184 J/g°C * (final temperature - 30°C)) = 0
Now we can solve this equation for the final temperature.
(334.72 J/°C * (final temperature - 100°C)) + (125.52 J/°C * (final temperature - 30°C)) = 0
334.72 J/°C * final temperature - 33472 J + 125.52 J/°C * final temperature - 3765.6 J = 0
(334.72 J/°C + 125.52 J/°C) * final temperature = 3765.6 J + 33472 J
460.24 J/°C * final temperature = 37237.6 J
final temperature = 37237.6 J / 460.24 J/°C
final temperature ≈ 80.88°C
Therefore, the final temperature of the mixture will be approximately 80.88 degrees Celsius.