A piece of copper ball of mass 20g at 200oc is placed in a copper calorimeter of mass60g containing50g of water at 30oc .Ignoring heat losses,calculate the final steady temperature of the mixture ,(specific heat capacity of water = 4.2Jkg)specific heat capacity of copper =0.4Jkg
To calculate the final steady temperature of the mixture, we can use the principle of conservation of heat. The heat lost by the hot copper ball is equal to the heat gained by the cold water and calorimeter.
First, let's calculate the heat lost by the copper ball using the formula:
Heat lost by the copper ball = mass of the copper ball * specific heat capacity of copper * (final temperature - initial temperature)
Given:
Mass of the copper ball = 20 g
Specific heat capacity of copper = 0.4 J/g°C
Initial temperature of the copper ball = 200°C
Let's calculate the heat lost by the copper ball:
Heat lost by the copper ball = 20 g * 0.4 J/g°C * (final temperature - 200°C)
Next, let's calculate the heat gained by the water and the calorimeter. The heat gained by the water can be calculated using the formula:
Heat gained by the water = mass of the water * specific heat capacity of water * (final temperature - initial temperature)
Given:
Mass of the water = 50 g
Specific heat capacity of water = 4.2 J/g°C
Initial temperature of the water = 30°C
Let's calculate the heat gained by the water:
Heat gained by the water = 50 g * 4.2 J/g°C * (final temperature - 30°C)
Finally, since there are no heat losses, the heat lost by the copper ball is equal to the heat gained by the water and the calorimeter. Therefore, we can set up an equation:
20 g * 0.4 J/g°C * (final temperature - 200°C) = 50 g * 4.2 J/g°C * (final temperature - 30°C)
Now we can solve this equation to find the final steady temperature of the mixture. We'll start by simplifying the equation:
8 (final temperature - 200) = 210 (final temperature - 30)
Expanding and simplifying:
8 final temperature - 1600 = 210 final temperature - 6300
Rearranging:
8 final temperature - 210 final temperature = -6300 + 1600
-202 final temperature = -4700
Dividing both sides by -202 to solve for the final temperature:
final temperature = -4700 / -202
final temperature ≈ 23.27°C
Therefore, the final steady temperature of the mixture is approximately 23.27°C.