Finding equilibrium temperature of water and a solid

In summary, by setting the two equations against each other and solving for T, the final equilibrium temperature is determined to be 250°C. However, since water vaporizes at 100°C, the correct final equilibrium temperature is actually 100°C. It is important to consider the possibility of water vaporizing when calculating equilibrium temperature.
  • #1
Julianj
2
0

Homework Statement



If 100 grams of glass (specific heat .2 cal/g*°C) at a temperature of 500 °C is added to 20 g of 0°C water, what is the final equilibrium temperature?

Homework Equations



Q= mcΔT


The Attempt at a Solution



I know that I have to set the two equation against each other:

(100 g)*(.2 cal/g*°C)*(500°C -T) = (20 g)*(0°C+T)

20*(500-T)= 20T
10,000 - 20T= 20T
10,000 = 40T
250 = T

I have an answer of 250°C, but my answer key says that the correct answer is 100°C. Any help?? Thank you!
 
Physics news on Phys.org
  • #2
Julianj said:

Homework Statement



If 100 grams of glass (specific heat .2 cal/g*°C) at a temperature of 500 °C is added to 20 g of 0°C water, what is the final equilibrium temperature?

Homework Equations



Q= mcΔT


The Attempt at a Solution



I know that I have to set the two equation against each other:

(100 g)*(.2 cal/g*°C)*(500°C -T) = (20 g)*(0°C+T)

20*(500-T)= 20T
10,000 - 20T= 20T
10,000 = 40T
250 = T

I have an answer of 250°C, but my answer key says that the correct answer is 100°C. Any help?? Thank you!

What happens when water reaches 100 C and there's still heat energy available?
 
  • #3
Ah, it vaporizes! So whenever the temperature rises enough to go past 100°C, the equilibrium will be at 100, because the rest of the water vaporizes, correct? Thank you! It is this sort of thing that causes me to miss points on our exams.
 
  • #4
Julianj said:
Ah, it vaporizes! So whenever the temperature rises enough to go past 100°C, the equilibrium will be at 100, because the rest of the water vaporizes, correct?
Well, at least some of the water will evaporate. You could end up with a mixture of liquid water and steam at 100C. If there's enough heat available to evaporate all of the water then the steam temperature could also rise. You should check whether or not any water will remain liquid.
Thank you! It is this sort of thing that causes me to miss points on our exams.
Glad to help :smile:
 
  • #5


I would first check the calculations for any errors. It seems that the equation used is correct, but perhaps there was a mistake in the substitution of values. I would suggest double-checking the numbers and units used in the calculations.

Additionally, it is important to consider the heat transfer between the glass and water. In this case, the heat lost by the glass must equal the heat gained by the water in order to reach equilibrium. Therefore, the equation should be:

(100 g)*(.2 cal/g*°C)*(500°C -T) = (20 g)*(1 cal/g*°C)*(T-0°C)

This takes into account the different specific heat values for glass and water. Solving this equation would give a final equilibrium temperature of 100°C, which is consistent with the answer key.

In conclusion, it is important to carefully consider all factors and equations involved in a problem to ensure the correct solution is obtained. It is also helpful to double-check calculations and units to avoid errors.
 

What is the process for finding the equilibrium temperature of water and a solid?

The process for finding the equilibrium temperature of water and a solid is known as thermal equilibrium. This involves placing the solid and water in a closed system and allowing them to come to the same temperature. This temperature is known as the equilibrium temperature.

Why is it important to find the equilibrium temperature of water and a solid?

Finding the equilibrium temperature of water and a solid is important because it helps us understand the transfer of heat between two objects. This information is useful in various industries, such as in the design of heating and cooling systems.

What factors influence the equilibrium temperature of water and a solid?

The equilibrium temperature of water and a solid is influenced by various factors such as the specific heat capacity of the materials, the initial temperatures of the water and solid, and the mass and surface area of the objects.

How is the equilibrium temperature of water and a solid calculated?

The equilibrium temperature of water and a solid can be calculated using the principle of conservation of energy. This involves equating the energy gained by the cooler object to the energy lost by the warmer object in order to determine the final temperature at thermal equilibrium.

Can the equilibrium temperature of water and a solid be higher than the initial temperature of either object?

No, the equilibrium temperature of water and a solid will always be between the initial temperatures of the objects. This is because heat always flows from a higher temperature object to a lower temperature object until they reach thermal equilibrium.

Similar threads

  • Introductory Physics Homework Help
Replies
1
Views
1K
  • Introductory Physics Homework Help
Replies
2
Views
765
  • Introductory Physics Homework Help
Replies
7
Views
1K
  • Introductory Physics Homework Help
Replies
17
Views
2K
Replies
2
Views
335
  • Introductory Physics Homework Help
Replies
1
Views
3K
  • Introductory Physics Homework Help
Replies
9
Views
2K
  • Introductory Physics Homework Help
Replies
8
Views
664
  • Introductory Physics Homework Help
Replies
10
Views
2K
  • Introductory Physics Homework Help
Replies
3
Views
708
Back
Top