How does temperature affect the average velocity of particles in a gas?

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SUMMARY

The discussion centers on the relationship between temperature and the average velocity of gas particles, specifically in an ideal gas scenario. When the temperature of the gas increases from 304 K to 608 K, the average speed of the gas molecules does not double, as initially assumed. Instead, the correct relationship is that the average velocity is proportional to the square root of the temperature ratio, leading to the conclusion that v2/v1 equals the square root of (608 K / 304 K), which simplifies to approximately 1.414, not 2.

PREREQUISITES
  • Understanding of the Ideal Gas Law (PV=nRT)
  • Basic knowledge of kinetic theory of gases
  • Familiarity with temperature and kinetic energy relationships
  • Ability to perform mathematical operations involving square roots
NEXT STEPS
  • Study the Ideal Gas Law and its applications in thermodynamics
  • Learn about the kinetic theory of gases and its implications for molecular motion
  • Explore the mathematical derivation of the relationship between temperature and average velocity
  • Investigate the concept of root mean square speed in gas particles
USEFUL FOR

Students studying thermodynamics, physics educators, and anyone interested in the behavior of gases under varying temperature conditions.

Runaway
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Homework Statement



A sample of an ideal gas is in a tank of constant volume. The sample absorbs heat energy so that its temperature changes from
304 K to 608 K.
If v1 is the average speed of the gas
molecules before the absorption of heat and
v2 their average speed after the absorption of
heat, what is the ratio
v2/v1 ?

Homework Equations


PV=nRT

The Attempt at a Solution


I thought that the answer would be 2 because temperature is in effect the average velocity of the molecules in the gas, and the temperature doubles, so therefore the average velocity would double making V2/V1=2 but the online assignment said that answer was wrong
 
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Runaway said:

The Attempt at a Solution


I thought that the answer would be 2 because temperature is in effect the average velocity of the molecules in the gas,

Why do you think so? How much is the average velocity of the molecules in the gas ?

ehild
 
It may help to know that temperature is proportional to the kinetic energy of the molecules, not directly proportional to velocity.
 

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