# Measurement of Temperature question.

1. Jan 9, 2012

### lionely

A mercury thermometer with only the 0 degree Celsius and 100 degree Celsius markings on it was given to a student, and the student was asked to use it to estimate the temperature of a block of ice cream.

I'm not sure, because the scale stops at 0 and mostly likely the temperature of ice cream is below 0. What should I do?

Can someone give me a hint please?

2. Jan 9, 2012

### sandy.bridge

What if we put the ice-cream in a closed system and measure the temperature change in the system?

3. Jan 9, 2012

### lionely

Oh like if we put it in a plastic dish that was let's say 50 degree celcius and then we put the ice cream in and then it dropped to 10 then the temperature of the ice cream is -40?

4. Jan 9, 2012

### sandy.bridge

Or melt a bowl of ice cream until its temperature is 10C, then place the frozen ice cream in the melted ice cream and allow it to reach thermal equilibrium. I would also ensure the mass of both are equal.

5. Jan 9, 2012

### lionely

Oh Thank you!

6. Jan 9, 2012

### sandy.bridge

I think it would be something like:
$$T_{final, system}=(T_{initial, melted}+T_{initial, frozen})/2$$

7. Jan 9, 2012

### lionely

I'm sorry I don't really understand that equation why would you divide it by 2?

8. Jan 9, 2012

### sandy.bridge

Dividing it by two averages the temperatures of the melted and frozen.

9. Jan 9, 2012

### lionely

Oh I see, sorry xD. So from if the melted was 10C and the frozen was -30C

then final temp would be (10C + (-30C))/2= -10C ?

10. Jan 9, 2012

### sandy.bridge

Yes, and if that were the case you would still not be able read it on the thermometer unless the final temperature of the system>0. So if you get a reading of zero, you may have to further increase the temperature of the melted ice cream. Does that make sense?

11. Jan 9, 2012

### lionely

So for the student to read it the ice cream must melt until about, 20C
I'm going to change my assumption and assume the frozen is about -15C

so it would be

(20C -15)/2 = 2.5C

12. Jan 9, 2012

### lionely

But is it right it to make such an assumption?

13. Jan 9, 2012

### sandy.bridge

You don't have to make an assumption. For example, you measure the initial temperature of the melted ice cream to be
$$T_{initial, melted}=10$$.
You then combine the melted ice cream with the frozen ice cream and allow the system to reach equilibrium at which point you will measure
$$T_{final, system}$$
Can you now see how to determine the initial temperature of the frozen? Btw, this is assuming a closed system and is merely an approximation..

14. Jan 9, 2012

### lionely

Oh yes I see how you would get the initial frozen simple mathematics stupid me. Just

find the unknown with the two known. I think I fully understand now.