A piece of copper ball of mass 20g at 200 degree centigrade is placed in a copper calorimeter of mass 60g containing 50g of water at 30 degree centigrade. Ignoring heat losses calculate the final temperature of the mixture
20 * 377 * (200 - t) = [(50 * 4190) + (60 * 377)] * (t - 30)
To calculate the final temperature of the mixture, we can use the principle of energy conservation and the equation of heat transfer:
Heat gained by the water = Heat lost by the copper ball
The formula for heat transfer is given by:
Q = m * c * ΔT
Where:
Q is the heat transfer
m is the mass of the substance
c is the specific heat capacity of the substance
ΔT is the change in temperature
First, let's calculate the heat lost by the copper ball:
Mass of the copper ball (m1) = 20g
Initial temperature of the copper ball (T1) = 200°C
Specific heat capacity of copper (c1) = 0.39 J/g°C (specific heat capacity of water)
Heat lost by the copper ball (Q1) = m1 * c1 * (Tinitial - Tfinal)
Now, let's calculate the heat gained by the water:
Mass of the water (m2) = 50g
Initial temperature of the water (T2) = 30°C
Specific heat capacity of water (c2) = 4.18 J/g°C (specific heat capacity of copper)
Heat gained by the water (Q2) = m2 * c2 * (Tfinal - Tinitial)
Since the heat gained by the water is equal to the heat lost by the copper ball (ignoring heat losses):
Q1 = Q2
m1 * c1 * (T1 - Tfinal) = m2 * c2 * (Tfinal - T2)
Now we can solve this equation to find the final temperature of the mixture (Tfinal). Let's substitute the given values:
(20g * 0.39 J/g°C * (200°C - Tfinal)) = (50g * 4.18 J/g°C * (Tfinal - 30°C))
After multiplying and rearranging the equation, we get:
7.8(200 - Tfinal) = 209(Tfinal - 30)
Simplifying further:
1560 - 7.8Tfinal = 209Tfinal - 6270
Combining like terms:
216.8Tfinal = 7830
Finally:
Tfinal = 7830 / 216.8
Tfinal is approximately 36.135°C.
Therefore, the final temperature of the mixture is approximately 36.135°C.