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Say I have a beaker of water at 30 degree celsius. Now I take a cup of water from that beaker. That cup of water is also 30 degrees but since a smaller sample has lesser no.of molecules and therefore lesser total kinetic energy and lesser thermal energy shouldn't it be at a lower temperature?

EDIT: Since total kinetic energy of the smaller sample decrease shouldn't the average also decrease, hence decreasing temperature? Can someone please explain?

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    $\begingroup$ Temperature doesn't measure total kinetic energy of an object, it measures the mean kinetic energy per particle in the object. $\endgroup$
    – The Photon
    Commented Feb 7, 2022 at 6:04
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    $\begingroup$ Let me try an analogy. Two objects, one 'small', one 'large', travel at the same velocity. Clearly the 'larger' one has more kinetic energy, yet both travel at the same velocity. $\endgroup$
    – Gert
    Commented Feb 7, 2022 at 6:06
  • $\begingroup$ I have edited the questionEDIT:Since total kinetic energy of the smaller sample decrease shouldn't the average also decrease, hence decreasing temperature? Can someone please explain? $\endgroup$
    – AJknight
    Commented Feb 7, 2022 at 6:16
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    $\begingroup$ 10 people in a room each have 2 dollars. The total amount of money in the room is 20 dollars, and the average per person is 2 dollars. Then the people split off into two rooms. The total amount of money in each room is 10 dollars, but the average per person is still 2 dollars. $\endgroup$
    – d_b
    Commented Feb 7, 2022 at 6:42

2 Answers 2

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As @ThePhoton said, temperature is a measure of the mean kinetic energy per particle.

Suppose you had 1050 kinetic-energy-units and 210 particles. What is the temperature?

When you took a cup of water, you took kinetic energy and a proportional number of particles away.
Suppose you took away 50 kinetic-energy-units and 10 particles.

Compare

$$\frac{(1000+50)}{(200+10)}, \quad \frac{1000}{200},\mbox{ and }\quad \frac{50}{10}$$

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  • $\begingroup$ So what you mean to say is that the mean of kinetic energies of the larger sample and smaller sample end up being the same?Am I right? $\endgroup$
    – AJknight
    Commented Feb 7, 2022 at 6:36
  • $\begingroup$ @AJknight Yes.. that's why, when in thermal equilibrium, they all have the same temperature. $\endgroup$
    – robphy
    Commented Feb 7, 2022 at 7:01
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but since a smaller sample has lesser no.of molecules and therefore lesser total kinetic energy and lesser thermal energy shouldn't it be at a lower temperature?

No, because the temperature reflects the average kinetic energy, not the total kinetic energy. And the average kinetic energy of the beaker of water and the cup of water when it was immediately taken from it would be the same.

Hope this helps.

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