# Help with thermodynamics

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Let's say we have $m$ kg of oxygen at $T_1$ K. After heating the oxygen, it did $A$ J of work. Find the temperature to which the oxygen was heated. $p=const$. This is all simple of course, using the $A=p(V_2-V_1)=\frac{m}{M}R(T_2-T_1)$ formula. Now we are able to find how much did $U$ change using the $U=\frac{3m}{2M}R(T_2-T_1)$ formula. Since $Q=U+A$ according to the first law of thermodynamics, $Q=\frac{5m}{2M}R(T_2-T_1)$. Here's the problem:

$Q=cm(T_2-T_1)=\frac{5m}{2M}R(T_2-T_1)$

from witch

$c=\frac{5R}{2M}$. Numbers don't show that the given formula is correct nor is it correct when we take $V=const, c=\frac{3R}{2M}$. So, my question is: Why is the above all wrong, and how do you calculat c with ideal gases and how to make a small triangle appear in front of $T$?

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Oxygen is a diatomic molecule and hence has 6 degrees of freedom, 3 translational, 2 rotational and 1 vibrational. Both rotational degrees of freedom will contribute to Cv but the vibrational one won't (at least at normal temperatures).

For a diatomic Cv = 5/2R, Cp =7/2R

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