# Determining specific heat

1. Jul 15, 2007

### trah22

1. The problem statement, all variables and given/known data

an aluminum calorimeter with a mass of 100g contains 250g of water. THe calorimeter and water are in thermal equilibrium at 10 degrees celcius. Two metallic blocks are placed into the water. One is copper of 50g at 80celcius. The other is block is 70g and originally at temp of 100Celcius. The entire system stablilizes at a final temp of 20celcius. Determine the specific heat of the unknown sample.
2. Relevant equations
Q=mC(changeofT)
so c=Q/m(changeofT)
Qcold=-Qhot

3. The attempt at a solution

MwCw(10celcius)+MaCa(10celcius)=-McuCcu(20-80)-MukCuk(20-100)
so
250g(4186J/Kg)(10)+100(900J/Kg)(10)=-50(387J/kg)(-60)-MukCuk(-80)

im not sure if i set up the unknows correctly (Mu=mass of unknown and Cuk=specific heat of unknow)...... can anyone help me out

2. Jul 16, 2007

### cepheid

Staff Emeritus
I think you are doing it correctly, and you're doing it all in one equation, whereas I was thinking of breaking it down into steps as follows. It's been a while since I've done this type of problem, but it seems to be that this is what needs to be done:

1. Calculate the total amount of energy transferred from the blocks to the calorimeter (this is the left hand side of the equation you have written down).

$$Q_{\textrm{tot}} = m_{\textrm{H2O}}c_{\textrm{H2O}} \Delta T_{\textrm{cal}} + m_{\textrm{Al}}c_{\textrm{Al}} \Delta T_{\textrm{cal}}$$

where [itex] \Delta T_{\textrm{cal}} [/tex] is the change in temperature of the calorimeter equal to 20 C - 10 C = +10 C

Now you know how much energy was transferred from the two blocks to the calorimeter. Unfortunately, some of this came from the copper block, and some from the unknown block. You know the specific heat of copper, so you can figure out how much heat was transferred from the copper:

$$Q_{\textrm{Cu}} = m_{\textrm{Cu}}c_{\textrm{Cu}} \Delta T_{\textrm{Cu}}$$

Then you can subtract this from the total heat in order to determine how much came from the unknown block (this is equivalent to isolating the unknown term on the right hand side of your equation):

$$Q_{\textrm{unk}} = Q_{\textrm{tot}} - Q_{\textrm{Cu}}$$

And, of course, since you know the mass of the unknown block and its change in temperature, you can easily calculate c_unk from Q_unk.

Last edited: Jul 16, 2007
3. Jul 16, 2007

### trah22

i think i got thanks for the explanation