# Thermal Energy Question

#### froese14

A 150g steel spoon (constant = 420J/kg degrees Celsius) initially at 19 degrees Celsius is placed into a 250mL cup of water at 89 degrees Celsius. When both objects reach the same temperature what temperature will that be?

#### Woody

You need to know the specific heat capacity of the steel and of the water.
The specific heat capacity is the amount of energy (Joules) required to change the temperature of (1kg of) a material (by 1 degree Celsius).

Now you have a couple of options.
You could do an iterative solution.
As a starter work out how many Joules are required to raise the temperature of the spoon by 70 degrees Celsius.
Then work out how much colder the water will be if you remove that number of joules from it.
Now find the number of Joules needed to raise the temperature of the spoon by the lower amount required to match the colder temperature of the water you have just found.
Then find the (slightly warmer) temperature of the water that results from transferring this lower number of joules to the spoon,
Now find the number of Joules needed to raise the temperature of the spoon by the amount required to match the (slightly warmer) temperature of the water you have just found.
and then repeat and repeat this calculation again and again, until the change in temperature and the change in the number of joules transferred, between one calculation to the next, is small enough not to matter.
The final temperature of this (rather long winded) process will be the answer you are seeking.
However,
A much slicker way would be to define a pair of simultaneous equations, for the temperature changes verses joules transferred, and solve them to find the resultant temperature.

My guess is that your tutor would be looking for you to use the 2nd option,
but would accept the first option as a reasonable alternative.