Why Is My Calculation of Thermal Equilibrium Temperature Incorrect?

[crimesofparis]

I'm having some trouble with thermal energy problems. The first question goes like this.

200g of Al at 300 degrees C is placed into a 100g glass Calorimeter with 200g of water at 10 degrees C. What is the final equilibrium temperature of the system. The answer is 57.3 degrees C (the teacher always gives us the answers on homework).

I understand that the formula is mc*change in T=mc*change in T, but when I put in the equation my answer isn't even close. This is what I'm doing

2(742)(300-Tf)=2(4186)(10-Tf)

Can anyone tell me what I'm doing wrong?

I have a similar question about another problem.

An Al calorimeter, 100g, that contains 500g of water at 10degC has the following put into it simultaneously. 200g of brass at 150degC, 200g of silver at 200degC, 100g of copper at 100deg C. Assuming no water loss due to vaporization, determine the final equilibrium temperature. The answer is 19.9degC.

I have no idea where to start this one...

Any help would be appreciated.

 

[antonantal]

In the formula $$Q = mc{\Delta}T$$ that you use, $$T$$ is expressed in Kelvins, so you should transform your temperatures from Celsius degrees to Kelvins.

 

[m2003]

Hello,

It seems like you are having some trouble with thermal energy problems. Let me try to help you understand the concepts better.

First, let's review the formula for calculating thermal energy:

Q = mcΔT

Q represents the thermal energy, m is the mass of the substance, c is the specific heat capacity, and ΔT is the change in temperature.

For the first question, we have to find the final equilibrium temperature of the system. This means that the heat lost by the aluminum will be equal to the heat gained by the water and calorimeter. So, we can set up the equation as follows:

Qlost = Qgained

mcΔT = mcΔT

(200g)(0.902 J/g°C)(300°C - Tf) = (100g)(4.186 J/g°C)(Tf - 10°C)

Simplifying this equation will give you Tf = 57.3°C, which is the correct answer.

For the second question, we have to take into account the heat lost and gained by all the substances in the calorimeter. The equation will look like this:

Qlost = Qgained

[200g(0.902 J/g°C)(150°C - Tf) + 200g(0.235 J/g°C)(200°C - Tf) + 100g(0.385 J/g°C)(100°C - Tf)] = (500g)(4.186 J/g°C)(Tf - 10°C)

Solving this equation will give you Tf = 19.9°C, which is the correct answer.

I hope this helps you understand the concept better. Remember to always check your units and make sure they are consistent throughout the equation. Let me know if you need further clarification. Keep practicing and you will get the hang of it!