A piece of copper ball at 80 degree Celsius is quickly transferred into a copper calorimeter of mass 60g containing 200g of water at 25 degree celcuis . If the final temperature of the mixture is 55 degree celcuis .caculate the mass of the copper ball (ignore heat loss, take the shc of copper as 400 jk|k and that of water as 4200jklk
To calculate the mass of the copper ball, we can use the principle of heat transfer and the equation:
Q = mcΔT
Where:
Q = heat transferred
m = mass
c = specific heat capacity
ΔT = change in temperature
First, let's find the heat transferred from the copper ball to the water:
Q1 = mcΔT1
Given:
m1 = mass of the copper ball (unknown)
c1 = specific heat capacity of copper = 400 J/(kg·K)
ΔT1 = initial temperature difference = (final temperature of the mixture - temperature of the water) = (55°C - 25°C)
Next, let's find the heat transferred from the water:
Q2 = mcΔT2
Given:
m2 = mass of water = 200g = 0.2 kg
c2 = specific heat capacity of water = 4200 J/(kg·K)
ΔT2 = initial temperature difference = (final temperature of the mixture - temperature of the water) = (55°C - 25°C)
Since the heat transferred is the same for both substances, we can equate Q1 and Q2:
mc1ΔT1 = mc2ΔT2
Substituting the values:
m1 * 400 * (55 - 25) = 0.2 * 4200 * (55 - 25)
Now, we can solve for m1:
m1 = (0.2 * 4200 * (55 - 25)) / (400 * 30)
m1 = 0.7 kg
Therefore, the mass of the copper ball is 0.7 kg.