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Quote from: Bored chemist on 06/05/2022 12:58:48Quote from: hamdani yusuf on 06/05/2022 11:10:07Quote from: Bored chemist on 05/05/2022 08:31:51It can't be a very good attempt; it shows the solid as full of springs, and then it ignores potential energy.Perhaps the potential energy isn't counted as (doesn't contribute to) temperature.It is counted and does contribute.Why choose to be wrong about that?Then the definition would be false. Quote from: alancalverd on 05/05/2022 10:19:28What's to explain? The caption statement is almost correct: the definition of temperature is the average internal kinetic energy of a body. You can't explain a definition!
Quote from: hamdani yusuf on 06/05/2022 11:10:07Quote from: Bored chemist on 05/05/2022 08:31:51It can't be a very good attempt; it shows the solid as full of springs, and then it ignores potential energy.Perhaps the potential energy isn't counted as (doesn't contribute to) temperature.It is counted and does contribute.Why choose to be wrong about that?
Quote from: Bored chemist on 05/05/2022 08:31:51It can't be a very good attempt; it shows the solid as full of springs, and then it ignores potential energy.Perhaps the potential energy isn't counted as (doesn't contribute to) temperature.
It can't be a very good attempt; it shows the solid as full of springs, and then it ignores potential energy.
What's to explain? The caption statement is almost correct: the definition of temperature is the average internal kinetic energy of a body. You can't explain a definition!
It is counted and does contribute.
...an object absorbs 2 Joule of energy. 1 Joule is converted to potential energy, and 1 Joule is converted to kinetic energy. Another object with same mass absorbs 2 Joule of energy. 0 Joule is converted to potential energy, and 2 Joules is converted to kinetic energy....... the second object increases its temperature twice as much as the first object...
(i) The second object is not yet in thermal equillibrium. There isn't a equal partition of energy between the various modes or degrees of freedom it can support as forms of internal energy. As such its temperature is not well defined yet.
(ii) The "potential energy" you were considering was never one of the ways in which it can support internal energy, for example it might be gravitational potential energy due to lifting the object up higher. It had no relevance for temperature. (In which case, you would be right, gaining that sort of potential energy didn't make the first object hotter, it was 1 J of energy in some form that didn't change its temperature).
Then wait until it is well defined.
If we add thermal energy to an object but its temperature doesn't change, then according to the definition above, its internal kinetic energy doesn't change. Hence, the energy should be converted into something else, which can be external kinetic energy, external potential energy, internal potential energy, or combinations of those kinds of energy.Melting ice may cross our minds as an example.
How do you distinguish between internal and external energy?
As an example, an object absorbs 2 Joule of energy. 1 Joule is converted to potential energy, and 1 Joule is converted to kinetic energy.Another object with same mass absorbs 2 Joule of energy. 0 Joule is converted to potential energy, and 2 Joules is converted to kinetic energy.According to the definition above, the temperature of the object increases corresponding to the increase of kinetic energy. Hence the second object increases its temperature twice as much as the first object.
Quote from: hamdani yusuf on 07/05/2022 04:13:59As an example, an object absorbs 2 Joule of energy. 1 Joule is converted to potential energy, and 1 Joule is converted to kinetic energy.Another object with same mass absorbs 2 Joule of energy. 0 Joule is converted to potential energy, and 2 Joules is converted to kinetic energy.According to the definition above, the temperature of the object increases corresponding to the increase of kinetic energy. Hence the second object increases its temperature twice as much as the first object.Correct. An increase of internal potential energy would correspond to a partial or total change of state within the body. I encountered this when measuring radiation dose with a calorimeter. Dose is defined as energy aborbed per unit mass, and the principal concern for radiation protection and radiotherapy is the measurement of dose to water. For practical simplicity most primary standard calorimeters use graphite as the absorber because it is mechanically stable and has about a tenth of the specific heat capacity of water so undergoes a larger temperature change (a lethal dose of ionising radiation raises your body temperature by about 0.001 degree - my task was to measure that to ± 10-6K). One of my colleagues built a water calorimeter - rather less portable device but clearly worth directly measuring the quantity of interest rather than trying to derive it. Problem was that the water calorimeter generally measured about 3% less than the graphite calorimeter, though both were calibrated to ± 0.01%. I thought the difference was due to "virgin" water forming metastable polymers when irradiated, because the defect gradually decreased with extended irradiation to high doses but later work has revealed all sorts of complex chemistry possible with just H and O atoms and plenty of energetic photons.
- we'd expected everything to recombine in microseconds.
The fundamental idea is that the energy will automatically be re-distributed throughout the system, so that you have an equi-partition of energy in all the modes or degrees of freedom that the system can support. So, if you do wait, then some of the energy, the 2 J of internal kinetic energy will be passed to other modes of storing energy. Taking a generalised example, if your system supports kinetic energy of the particles and also potential energy in the bonds (or springs) between atoms then you end up with 1 J remaining as kinetic and 1 J being potential energy. i.e. The second object becomes exactly like the first object in your example.
At low enough temperatures, the heat capacities of the gases are the same- the heat that you add goes into making the molecules translate.So rises in the temperatures of the two gases are both the same.
But there comes a point (A few K, I think) where there is enough energy to make the N2 molecules rotate.(Not many people think about this, but rotational energy is quantised).
Why don't polyatomic gases rotate nor vibrate at low temperature?
Is vibrational energy also quantized?
QM is not important.
What's the minimum non-zero quantity of of rotational energy?