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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 
Senior Member Joined: Feb 2014 From: Louisiana Posts: 156 Thanks: 6 Math Focus: algebra and the calculus  
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 nontrivial 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 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  

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energy, measure, temperature, thermal 
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