# Temperature & Gas: Correct or Incorrect?

• dorothy
In summary: Incorrect, since the root mean square speed(c^2）is directly proportional to the temperature, but it will just affect the average kinetic energy, doubling the k.e., but not related to the potential energy.I think this is a 'trick' question. What is the average of all of the velocities of the particles in a (stationary) container of gas?The average of all the velocities of the particles in a stationary container of gas is zero.
dorothy
Homework Statement
Which of the following statements is/are correct when the absolute temperature of a gas is doubled?
(1) Average potential and kinetic energies of the molecules doubled.
(2) The gas volume will be doubled.
(3) The average velocity of the gas molecules will be increased but not doubled.
A. (1) only
B. (3) only
C. (1) and (2) only
D. (1) and (3) only
Relevant Equations
/
(1) Incorrect, since the root mean square speed(c^2）is directly proportional to the temperature, but it will just affect the average kinetic energy, doubling the k.e., but not related to the potential energy.

(2) Correct, since the volume of gas is directly proportional to the temperature

(3) Incorrect, since velocity is a vector, it is directional. Gas molecules move in different directions so the statement is not true.

These are my points but seems there is no such option. May I ask what is wrong with my attempt? Thank you.

dorothy said:
(2) Correct, since the volume of gas is directly proportional to the temperature
I must have missed something. Where does it say that the volume is allowed to change?

phinds said:
I must have missed something. Where does it say that the volume is allowed to change?
oh, so I should assume the volume is fixed if the question doesn’t mention about it. Is that right?

dorothy said:
oh, so I should assume the volume is fixed if the question doesn’t mention about it. Is that right?
That's certainly what I would do.

IMO the question is unclear/badly written. Have you given us the entire question, word-for-word?

dorothy said:
Homework Statement:: Which of the following statements is/are correct when the absolute temperature of a gas is doubled?
Some answers will depend on whether the gas is ideal or real. Do you know which it is supposed to be?

dorothy said:
(1) Average potential and kinetic energies of the molecules doubled.
The question won't apply to an ideal gas which has no potential energy.

dorothy said:
(2) The gas volume will be doubled.
That depends on
a) if the pressure is kep constant
b) whether the gas is ideal or real

dorothy said:
(3) The average velocity of the gas molecules will be increased but not doubled.
I think this is a 'trick' question. What is the average of all of the velocities of the particles in a (stationary) container of gas?

Or it could be badly written and actually mean 'average speed'.

dorothy said:
(1) Incorrect, since the root mean square speed(c^2）is directly proportional to the temperature, but it will just affect the average kinetic energy, doubling the k.e., but not related to the potential energy.
The answer depends on whether the gas is ideal or real.

dorothy said:
(2) Correct, since the volume of gas is directly proportional to the temperature
Only if the pressure is constant and the gas is ideal.

dorothy said:
(3) Incorrect, since velocity is a vector, it is directional. Gas molecules move in different directions so the statement is not true.1
Correct - but I think you have not fully picked-up the key point (see above)! Or ir may be a badly written question and is really about average spped.

Have you learned about both ideal and real gases? If not, you may be expected to answer the question on the assumption it is about only an ideal gas.

TSny
dorothy said:
so I should assume the volume is fixed
No, you don’t need to assume that. The question asks what you can deduce from the given fact. Since you are not told anything about the volume or pressure, before or after, you cannot deduce the volume doubles.
Steve4Physics said:
The question won't apply to an ideal gas which has no potential energy.
Including potential energy doesn't stop it being a valid statement for an ideal gas. Rather, it implies you should not assume an ideal gas.
Steve4Physics said:
Or ir may be a badly written question and is really about average spped.
Unfortunately, that seems to me the most likely.

dorothy said:
(1) Incorrect, since the root mean square speed(c^2）is directly proportional to the temperature, but it will just affect the average kinetic energy, doubling the k.e., but not related to the potential energy.
Have you discussed monatomic gasses, diatomic gasses, and the equipartition theorem yet?

dorothy said:
I should assume the volume is fixed if the question doesn’t mention about it. Is that right?
No, you generally shouldn't assume anything about the volume. The question is asking: if you double the temperature, will the volume always double? As others have pointed out, the volume doubles only under certain conditions, so you can't conclude that doubling the temperature necessarily results in the volume doubling.

Steve4Physics said:
The question won't apply to an ideal gas which has no potential energy.
If you double zero, it's still zero.

vela said:
If you double zero, it's still zero.
Yes indeed. And in fact I considered that when writing the post.

However I felt uncomfortable doubling something that was necessarily zero, so decided to phrase it the way I did.

vela said:
If you double zero, it's still zero.
I'm not aware of how the potential energy of an ideal gas is even defined. Am I missing something?

(OP has already ruled out this statement as incorrect, so I think it's fair game for discussion.)

Redbelly98 said:
I'm not aware of how the potential energy of an ideal gas is even defined.
Same as its definition for a non-ideal gas, but with the added fact that it is constant?

Last edited:
haruspex said:
Same as its definition for a non-deal gas, but with the added fact that it is constant?
Okay, fair enough.

Redbelly98 said:
I'm not aware of how the potential energy of an ideal gas is even defined. Am I missing something?

(OP has already ruled out this statement as incorrect, so I think it's fair game for discussion.)
One of the assumptions of an ideal gas is that the particles don't interact, so I'd just take the PE as zero.

vela said:
One of the assumptions of an ideal gas is that the particles don't interact, so I'd just take the PE as zero.
Yeah, I was initially thinking -- erroneously -- it would be undefined for noninteracting objects. But okay, if the forces between the particles are zero then it's just a constant. And then apply the usual convention of calling it zero in the limit of infinite separation.

vela

## What is the relationship between temperature and the kinetic energy of gas molecules?

The temperature of a gas is directly proportional to the average kinetic energy of its molecules. As the temperature increases, the kinetic energy of the gas molecules also increases, causing them to move faster.

## Does increasing the temperature of a gas always increase its pressure?

Increasing the temperature of a gas will increase its pressure if the volume of the gas is held constant. This is described by Gay-Lussac's Law, which states that the pressure of a gas is directly proportional to its absolute temperature when the volume is constant.

## Can a gas have a temperature of absolute zero?

No, a gas cannot have a temperature of absolute zero (0 Kelvin) because, at this temperature, the kinetic energy of the gas molecules would be zero, meaning they would be at a complete standstill. Absolute zero is a theoretical limit that cannot be reached in practice.

## How does temperature affect the volume of a gas?

According to Charles's Law, the volume of a gas is directly proportional to its absolute temperature when the pressure is held constant. This means that as the temperature of a gas increases, its volume also increases, and vice versa.

## Is the relationship between temperature and gas behavior the same for all gases?

The relationship between temperature and gas behavior is generally described by the Ideal Gas Law, which applies to ideal gases. However, real gases deviate from this behavior at high pressures and low temperatures, where intermolecular forces and the volume occupied by the gas molecules become significant.

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