Solving the Mystery of Helium's Temperature Increase

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SUMMARY

The discussion focuses on the relationship between helium's internal energy and its absolute temperature, specifically addressing a problem where helium's temperature is increased to double its internal energy. Starting from an initial temperature of 20°C, the correct final temperature is determined to be 313 K, which converts to 40°C. The key takeaway is that internal energy (U) is directly proportional to absolute temperature (T), and the conversion from Celsius to Kelvin is crucial for solving the problem accurately.

PREREQUISITES
  • Understanding of the relationship between internal energy and absolute temperature.
  • Knowledge of temperature conversion between Celsius and Kelvin.
  • Familiarity with the concept of proportionality in physics.
  • Basic thermodynamics principles related to gases.
NEXT STEPS
  • Study the principles of thermodynamics, focusing on internal energy and temperature relationships.
  • Learn about the Kelvin scale and its applications in scientific calculations.
  • Explore the properties of helium and other noble gases in thermodynamic contexts.
  • Practice solving problems involving energy and temperature conversions in various scenarios.
USEFUL FOR

This discussion is beneficial for physics students, educators, and anyone interested in thermodynamics, particularly those studying gas properties and energy transformations.

Runaway
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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


Homework Equations





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.
 
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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 :)
 

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