Having trouble with this heat transfer problem

In summary: You can calculate the heat energy needed by the glass thermometer and the mercury.This heat energy came from the water and the glass vial.
  • #1
xnitexlitex
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Homework Statement


When an immersion glass thermometer is used to measure the temperature of a liquid, the temperature reading will be affected by an error due to heat transfer between the liquid and the thermometer. Suppose you want to measure the temperature of 10 mL of water in a Pyrex glass vial thermally insulated from the environment. The empty vial has a mass of 5.0 g. The thermometer you use is made of Pyrex glass as well and has a mass of 18 g, of which 7 g is the mercury inside the thermometer. The thermometer is initially at room temperature (20.0°C). You place the thermometer in the water in the vial and, after a while, you read an equilibrium temperature of 27°C. What was the actual temperature of the water in the vial before the temperature was measured? The specific heat capacity of Pyrex glass around room temperature is 800 J/(kg K) and that of liquid mercury at room temperature is 140 J/(kg K).


Homework Equations


Qa = Qb
Q=mcΔT


The Attempt at a Solution


I've tried using Qwater+glass = Qthermometer+mercury and Qwater = Qpyrex + Qmercury. I think my problem is finding the ΔT's. I have ΔT = 7 for the pyrex and the mercury, but I can't determine where my Ti should go for the water. are my ΔT's for the myrex and mercury right?
 
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  • #2
I think the ΔT is 7 degrees for the glass thermometer+mercury.
You can calculate the heat energy needed by the glass thermometer and the mercury.
This heat energy came from the water and the glass vial.
Does this help?
 
  • #3
technician said:
I think the ΔT is 7 degrees for the glass thermometer+mercury.
You can calculate the heat energy needed by the glass thermometer and the mercury.
This heat energy came from the water and the glass vial.
Does this help?

Could you go into more detail, with equations if you can?
 

Related to Having trouble with this heat transfer problem

1. How do I know which heat transfer equation to use for a specific problem?

In order to determine which heat transfer equation to use, you must first identify the type of heat transfer involved. There are 3 types of heat transfer: conduction, convection, and radiation. Conduction occurs when heat is transferred through a solid object, convection occurs when heat is transferred through a fluid (liquid or gas), and radiation occurs when heat is transferred through electromagnetic waves. Once you have identified the type of heat transfer, you can then select the appropriate equation for that type of transfer.

2. Why is my heat transfer problem not balancing?

If your heat transfer problem is not balancing, it could be due to a number of reasons. One possibility is that you have made a mistake in your calculations or in setting up the problem. Another possibility is that there may be additional factors at play, such as heat loss or gain from the surroundings. It is important to carefully check your calculations and consider all relevant factors in order to balance the problem.

3. How do I account for changing temperatures in my heat transfer problem?

To account for changing temperatures in a heat transfer problem, you can use the concept of temperature gradients. Temperature gradients represent the change in temperature over a given distance. By considering the temperature gradients at different points in the system, you can accurately account for changing temperatures and their effect on the heat transfer.

4. What are the common assumptions made in heat transfer problems?

Some common assumptions made in heat transfer problems include assuming steady-state conditions, neglecting radiation effects, and assuming uniform temperature distributions. These assumptions may not always hold true in real-world situations, but they allow for simplification of the problem and still provide accurate results in many cases.

5. How can I check the accuracy of my heat transfer calculations?

To check the accuracy of your heat transfer calculations, you can compare your results to known values or experimental data. Additionally, you can perform sensitivity analyses by varying different parameters in your calculations to see how they affect the outcome. It is also helpful to have a second person review your calculations to catch any potential errors or mistakes.

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