A piece of copper of ball of mass 20g is placed in a copper calorimeter of mass 60g containing 50g of water at 30 degree Celsius ignoring heat losses, calculate the final steady temperature of the mixture. (SHC of water = 4.2j/g/k)
Not enough info. Need temp of copper and calorimeter.
PS. A copper calorimeter is about the dumbest thing I've ever heard of. The idea is to use an insulator and copper is about as non-insulating as it gets.
35.6
To solve this question, you need to consider the heat exchange between the copper ball, the calorimeter, and the water. The heat gained by the water and the calorimeter should be equal to the heat lost by the copper ball.
Here's the step-by-step solution:
1. Calculate the heat gained by the water using the formula:
Qwater = mwater * cwater * ΔT
where:
Qwater is the heat gained by water (in joules),
mwater is the mass of water (in grams),
cwater is the specific heat capacity of water (in j/g/°C),
ΔT is the change in temperature of the water (final temperature - initial temperature).
In this case, mwater = 50g, cwater = 4.2j/g/°C, and ΔT = final temperature - 30°C.
So, Qwater = 50g * 4.2j/g/°C * (final temperature - 30°C)
2. Calculate the heat gained by the calorimeter using the same formula:
Qcalorimeter = mcalorimeter * ccalorimeter * ΔT
where:
Qcalorimeter is the heat gained by the calorimeter (in joules),
mcalorimeter is the mass of the calorimeter (in grams),
ccalorimeter is the specific heat capacity of the calorimeter (in j/g/°C),
ΔT is the change in temperature of the calorimeter (final temperature - initial temperature).
In this case, mcalorimeter = 60g, ccalorimeter = the specific heat capacity of copper (which is approximately 0.39 j/g/°C), and ΔT = final temperature - 30°C.
So, Qcalorimeter = 60g * 0.39j/g/°C * (final temperature - 30°C)
3. Since the heat lost by the copper ball is equal to the heat gained by the water and the calorimeter:
Qcopper = Qwater + Qcalorimeter
From step 1 and step 2, we have:
20g * specific heat capacity of copper * (final temperature - 30°C) = 50g * 4.2j/g/°C * (final temperature - 30°C) + 60g * 0.39j/g/°C * (final temperature - 30°C)
4. Simplify the equation and solve for the final temperature:
(20g * specific heat capacity of copper - 50g * 4.2j/g/°C - 60g * 0.39j/g/°C) * (final temperature - 30°C) = 0
Note: The specific heat capacity of copper is approximately 0.39 j/g/°C.
Solve the equation to find the value of final temperature.
By following the above steps, you will be able to calculate the final steady temperature of the mixture.