# Problem with heat capacity of thermal system

1. Apr 4, 2015

### Pouyan

1. The problem statement, all variables and given/known data
a) a styrofoam cup contains 200g of water at 20 C.What will be the equilibrium temp of the system after 100g of silver,initially at 300 C,has been added?you may assume that the heat capacity of the cup is negligible and that no heat is lost to the surroundings.

(b) a further 100g of an unknown substance,also at 300 C is now added to the system and the temperature rises by a further 26 degrees celsius
what is the specific heat capacity of the unknown substance?(the specific heat of water is 4180 Jkg^-1 K^-1 and that of silver 240 J kg^-1 K^-1)

2. Relevant equations
a) Q before = Q after
Q before = Mass of water * C water * (T - 20)
Q after = Mass of silver * C silver * (300-T)

b) My problem is this part. I dont know how I can set up the equation when a new substance is added to this system. Would please someone help me with part b of this question?!

3. The attempt at a solution
a) T = 28 C

2. Apr 4, 2015

### SteamKing

Staff Emeritus
After the 200 g of water and the 100 g of silver in Part a) have reached thermal equilibrium, both are at the same temperature.

In Part b), you start with the equilibrium temperature from Part a) with the water and silver, but now you have added 100 g of an unknown material which raises the temperature of the water and silver by 26° C while the unknown substance is cooled from 300° C. This requires no special setup, just regular bookkeeping of the amount of heat added to the water and silver and the amount of heat lost by the mystery material.

3. Apr 4, 2015

### Pouyan

Thanks but I think so :

in this case :

Q before : (mass of water*Cw + mass of silver*Cs) * (28 + 26)
Q after : (mass of x * Cx )(300-26)

when I try to eject Cx from Q before= Q after, I get wrong value
The correct answer is Oxygen (908.9 J/kg/K)

What is wrong with this equation?!

4. Apr 4, 2015

### SteamKing

Staff Emeritus
The water and silver are already at a temperature of 28° C, before the unknown substance is added. The heat transfer from this unknown substance is going to raise the temperature of the water and silver by 26° C, not by (28° + 26°).

It's not clear how you determined the unknown substance was Oxygen, which, as far as I know, is a gas at a temperature of 300° C

5. Apr 5, 2015

### Pouyan

I get 1887 which is not the correct answer.... I dont know how I can solve it

6. Apr 5, 2015

### SteamKing

Staff Emeritus
I have no idea what 1887 means, what units it has, or how you got it.