# Specific Heat Capacity Practical: Thermal Equilibrium

Using specific heat capacity to find the final temperature of a mixture.

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Up Learn – A Level physics (aqa)

## Thermal Physics

Here we have a glass cup

It has a mass of 0.200 kilograms, this specific heat capacity, and a temperature of 20 degrees Celsius

If we pour in 0.100 kg of water, which has this specific heat capacity and temperature…

What is the temperature of the water and glass once they’re in thermal equilibrium?

Now, we know that during heating, energy is transferred from an object at a higher temperature to an object at a lower temperature

So, the glass transfers energy, and the water gains it

And we assume that all the energy transferred from the glass is gained by the water.

Next, we know that we can use this formula to calculate Q

So, we can substitute for Q using this

And now, we can begin to substitute in our values, starting with our values for water.

So, we substitute the value for the mass of water here…

We substitute the value for the specific heat capacity here…

And we know that the change in temperature is equal to the final temperature subtract the initial temperature

So, we can add our initial temperature here

And expanding the brackets, we calculate this to be equal to…

Expanding the brackets, we calculate this.

Next, we do the same with our values for the glass.

So, we substitute in our values here…

And this time, when we expand the brackets, we calculate this to be equal to…

Expanding the brackets, we calculate this

So, now we can calculate the final temperature, which is.

First, we collect like terms

Then, we divide by 588 to make the final temperature the subject…

And we calculate that the final temperature is 9.29 degrees Celsius.

So, this is the temperature of the water and glass in thermal equilibrium!