Verify Final Temperature of Cu-Water System?

[pmalayavech]

Homework Statement

Need a second person to help verify if answer is correct.

Copper with a mass of 300 g initially at 200 °C is added to water with an initial temperature of 10 °C and mass of 500 g. What is the final temperature of the system when they are in equilibrium?

ANSWER must be in JOULES

My variables

Cu specific heat: 385.112 J/kg C

Water specificheat: 4186 J

Homework Equations

Mm Cm (Tm - Tf) = Mw Cw (Tf-Tw)

The Attempt at a Solution

Mm Cm (Tm - Tf) = Mw Cw (Tf-Tw)

I convert g to kg for mass
500g to .500kg and 300g to .300kgnow plug equation and work the algebraic equation

(.300) (385.112)(200-tf) = (.500)(4186)(tf-10)

to

(23106.72-115.5336Tf)=(2093Tf-20930)

to

4036.72 = 2208.5336 Tf

to

19.93934799 = Tf

Tf= 19.9 J/kg C

 

[Basic_Physics]

Get the same answer but units ^oC.

 

[pmalayavech]

so its not in Joules? but Celsius?

 

[haruspex]

so its not in Joules? but Celsius?

Yes, the answer is a temperature, so it cannot be in Joules.
It is a good idea to include the units in the equations all the way through. This helps in two ways. It can show up dimensional mismatches (like Joules versus degrees) and also aids in conversion between different units of the same dimension (^oC v. ^oF).

 

[Nickie]

I would first check the units of the final answer to ensure that it is in Joules, as requested in the problem. The final answer is in degrees Celsius, so it is not in the correct units. I would also double check the calculations and make sure that all the numbers and units are correct. Additionally, I would suggest using more significant figures in the calculations to ensure accuracy. Lastly, I would recommend using the correct specific heat values for copper and water, which are 0.385 J/g C and 4.186 J/g C, respectively. With these corrections, the final temperature would be approximately 21.1 °C. I would also suggest having a second person check the calculations to verify the answer.