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Since temperature is just average energy per mole why is it a fundamental quantity ?
Can't we simply have the unit of temperature as Joule / mole ?
Can't we simply have the unit of temperature as Joule / mole ?
Then what does temperature represent? I'm convinced that it is not a fundamental quantity and that it can be represented in other units. Why is there a need to have Kelvin as its basic unit?Temperature is not average energy per mole, so it couldn't possibly be measured in J/mol.
Since temperature is just average energy per mole why is it a fundamental quantity ?
Can't we simply have the unit of temperature as Joule / mole ?
Temperature isn't defined to be average energy, but it is proportional to it for an ideal gas.
The definition of temperature for a system is this
[itex]\dfrac{1}{T} = \dfrac{dS}{dU}[/itex] (with volume and number of particles held constant)
where [itex]S[/itex] is the entropy of the system. You can, as you suggest, choose units in which [itex]S[/itex] is dimensionless (a pure number), and then temperature has the same units as energy. In the usual units, temperature is given a pretty much arbitrary scale, and then this scaling factor is incorporated into the definition of entropy, so that the defining equation for temperature in terms of entropy continues to hold.
There are most probably historical reasons as to why the SI commitee chose to keep a base unit for temperature.Okay, that makes it much clearer. Thank You!
But I still do not understand why give temperature its own scale and not make its unit same as energy. Is it because of convenience i.e the Kelvin and Celsius scales provide more sensible numbers?
To put it simply: temperature is the tendency of an object to give off heat to another object. Take two isolated systems A and B and put them in contact such that they can exchange energy only in the form of heat, then heat will flow from A to B if and only if ##T_\mathrm{A} > T_\mathrm{B}##. In the same conditions, the systems will be said to be in thermal equilibrium if there is no net flow of heat from one to the other, in which case we must have that ##T_\mathrm{A} = T_\mathrm{B}##.So what does temperature represent physically?
Yes, you are right about my doubt. I don't know why it is bothering me so much but anyways I want to clear it up."Temperature", as you just said, measures the average speed of the molecules, relative to the speed of the center of mass. You seem to be very concerned over whether it is a "fundamental" quantity or not. I'm not sure what you mean by "fundamental" quantity, but it looks like you are talking about having a "unit" of measure (as in "meters") rather than "derived" (as in "meters per second").
Yes, I think meter is defined in terms of speed of light so distance being a derived quantity. So among distance, time and speed we only need two to be fundamental, other can be derived.Do you not understand that this is a purely arbitrary convention? Many advanced physics papers assume a system of measures in which speed is "fundamental" (because it has a "natural" unit, c) and distance is "derived".
No, it's not, for a number of reasons. First off, you should have said kinetic energy, not speed. Helium and argon at the same temperature have rather different average speeds. Kinetic theory presents a nice simple model for an ideal gas (some engineers use the term "perfect gas")."Temperature", as you just said, measures the average speed of the molecules, relative to the speed of the center of mass.
No, it's not, for a number of reasons. First off, you should have said kinetic energy, not speed. Helium and argon at the same temperature have rather different average speeds. Kinetic theory presents a nice simple model for an ideal gas (some engineers use the term "perfect gas").
So what's wrong with looking at temperature as energy?
Issue #1: Energy is an extensive property while temperature is an intensive one.
Okay, thank you very much. Much of my doubt regarding what is temperature is cleared.
I still have doubt regarding fundamental and derived quantity
I believed that if some physical property can be written in terms of fundamental quantities, it should be derived and cannot have its own unit. So here temperature can be written in terms of joule i.e. 1/T = dS / dU so it should be joule. But turns out that I'm wrong. You can have a fundamental quantity even if it is expressible in terms of fundamental quantities, right?
That is true, but it does not really explain why that occurs.Temperature tells you the direction that energy will spontaneously flow between two bodies. The thermodynamic definition of temperature implies that entropy will increase when energy moves from a hot body to a cold body. Therefore, energy moves from a hot body to a cold body.
That is true, but it does not really explain why that occurs.
Heat flows spontaneously from a body at higher temperature to a body at lower temperature because the average translational kinetic energy of the molecules in the hotter body is greater than the average translational kinetic energy of the molecules in the cooler one. This is true not only for ideal gases but for all matter.
Right.Two objects at exactly the same temperature can have very different specific heats, and two objects with the same amount of energy (per mole or whatever) will not automatically be at the same temperature.