My Math Forum Temperature as a measure of thermal energy

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 April 29th, 2015, 02:47 PM #1 Senior Member     Joined: Feb 2014 From: Louisiana Posts: 156 Thanks: 6 Math Focus: algebra and the calculus Temperature as a measure of thermal energy If temperature measures the average internal kinetic energy of an object, then how does this measure thermal energy, which is the total internal kinetic energy of an object?
 April 29th, 2015, 04:11 PM #2 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 It doesn't. A 2 kg mass with a given temperature contains twice the thermal energy of a 1 kg mass with the same temperature.
April 29th, 2015, 05:58 PM   #3
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Quote:
 Originally Posted by Country Boy It doesn't. A 2 kg mass with a given temperature contains twice the thermal energy of a 1 kg mass with the same temperature.
Okay, that makes sense. Then how do we measure thermal energy if don't do it with temperature?

 April 30th, 2015, 01:29 AM #4 Senior Member   Joined: Apr 2014 From: Glasgow Posts: 2,157 Thanks: 732 Math Focus: Physics, mathematical modelling, numerical and computational solutions The internal energy estimate is non-trivial because it depends on the type of medium (solid, liquid, gas, plasma). For ideal gases the internal energy can be determined using $\displaystyle U=mc_PT$ where U = internal energy (J), m = mass of subtance (kg), c_P = heat capacity of substance (J/kg/K) and T = temperature of substance (K). It can also be used as a crude estimate for other kinds of medium.
April 30th, 2015, 05:18 AM   #5
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Quote:
 Originally Posted by Country Boy It doesn't. A 2 kg mass with a given temperature contains twice the thermal energy of a 1 kg mass with the same temperature.
For a given substance, yes. But if the substances are different you need to take heat capacity into account.

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