500g of water at 100°c is mixed with 300g of water at 20°c.specific heat capacity of water is 4.2Jg°c.find the final temperature of mixture.
(Physics)
70o C
To find the final temperature of the mixture, we can use the principle of conservation of energy.
Step 1: Calculate the heat gained or lost by each of the water samples:
The heat gained or lost by an object can be calculated using the equation:
Q = mcΔT
where Q is the heat gained or lost, m is the mass of the object, c is the specific heat capacity of the substance, and ΔT is the change in temperature.
For the 500g of water initially at 100°C:
Q1 = (500g) * (4.2 J/g°C) * (final temperature - 100°C)
For the 300g of water initially at 20°C:
Q2 = (300g) * (4.2 J/g°C) * (final temperature - 20°C)
Step 2: Apply the principle of conservation of energy:
According to the principle of conservation of energy, the total heat lost by one sample of water should equal the total heat gained by the other sample of water. Therefore,
Q1 = -Q2
Step 3: Solve for the final temperature:
Substitute the equations for Q1 and Q2 into the conservation equation:
(500g) * (4.2 J/g°C) * (final temperature - 100°C) = - (300g) * (4.2 J/g°C) * (final temperature - 20°C)
Simplify and solve for the final temperature.
500 (100-T) = 300 (T-20)
does not matter what the stuff is as long as it does not change phase (it was not steam at 100).