# Solving the Mystery of Helium's Temperature Increase

• Runaway
In summary, the special property of helium states that its internal energy is directly proportional to its absolute temperature. When a flask of helium with a temperature of 20 C is heated to twice its internal energy, the resulting temperature is 313 C. This is determined by converting the temperature to the absolute scale, doubling the internal energy, and then converting back to Celsius.

## Homework Statement

Helium has the special property that its internal energy is directly proportional to its
absolute temperature. Consider a ﬂask of helium with a temperature of 20 C.
If it is heated to twice its internal energy, what will its temperature be?
1. 293 C
2. 313 C
3. 40 C
4. None of these
5. 293 K
6. 313 K

## The Attempt at a Solution

I have no idea how to solve this, I thought it would be 40C but the online homework said it was wrong.

Runaway said:
Helium has the special property that its internal energy is directly proportional to its
absolute temperature.

So Internal Energy is proportional to absolute temperature:

$$U(T) \propto T$$

Consider a ﬂask of helium with a temperature of 20 C.
If it is heated to twice its internal energy, what will its temperature be?
1. 293 C
2. 313 C
3. 40 C
4. None of these
5. 293 K
6. 313 K
What scale would we use for absolute temperature? Convert 20C to that scale. Let the internal energy be U. If you double the internal energy, what happens to the absolute temperature? Convert that temperature back to Celsius to see if it fits with any of the suggested answers. Hint: it is not "4. None of these".

AM

2. 313 C
I accidentally skipped over the absolute temp. part, thanks for your help :)