heat capacity in kelvin vs celsius [closed]








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I understand 
Fact 1) Average kinetic energy of an atom in a noble gas is proportional to the temperature in Kelvin.


Fact 2) Average kinetic energy of an atom is not linearly proportional to temperature in Celsius or Fahrenheit. 


Fact 3) The heat capacity equation 


delta q = mc delta T 


shows increase in energy is linearly proportional to temperature. 


However, Textbooks frequently use this equation in degrees Celsius. How is this not a contradiction of Fact 2?


Thanks




If we for sake of simplicity assume the heat capacity is temperature independent, then the thermal content, expressed as functions of $K$, resp. $^{\circ}C$, are 2 parallel lines:


$$Q = C \cdot T $$
$$Q = C \cdot (t + 273.15) = C \cdot t + C \cdot 273.15)$$


Heat capacity C=dQ/dT, resp. C=dQ/dt is their slope. Slopes of parallel lines are equal.


But the kinetic energy $E$ of particles, proportional to thermal energy $Q$ ( as generally, not all thermal energy is kinetic\* ) is proportional to T, but not t.


$$\frac{E}{T} = \frac{a \cdot Q}{T} = a \cdot C$$
$$\frac{E}{t} = \frac{a \cdot Q}{t} = a \cdot C \cdot \frac{t + 273.15}{t}= a \cdot C \cdot (1 + \frac{273.15}{t})$$ 




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\*) I missed the noble gas mentioning. Well, for noble gases, the amounts of their thermal and kinetic energy is almost identical.


The very subtle difference is


* Their slight non-ideality, caused by non-zero intermolecular interaction of their atoms, like collision potential energy and van der Waals forces.
* Electron excitation and ionization at high and very high temperatures.


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