What is the temperature dependency of p/T in the ideal gas? [closed]








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This is about the ideal gas equation $$pV=nRT$$ to plot ${p}\over{T}$ against $T$, where ${nR}\over{V}$ is constant. How would this graph look like?




See the following:


$$PV = nRT \implies \frac PT = \frac{nR}{V} = \text{const.}$$


So whatever you do with $T$, $P/T$ won't change, so it would be a constant horizontal line.


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Firstly, rearrange the equation to get $\frac{p}{T}$ in the left hand side:
$$\frac{p}{T} = \frac{nR}{V}$$


As the question says, $\frac{nR}{V}$ is always a constant. So, $\frac{p}{T}$ is also a constant. In other words, I double the temperature, I double the pressure as well, still giving me $\frac{p}{T}$, to make sure $\frac{nR}{V}$ is always constant.


So if one were to draw graph, because is always one value, even if we change the value of $T$, this has to mean that a graph of $\left(\frac{p}{T}\right)$ against $(T)$, will give a straight line graph with gradient $0$, and intersecting the $y$ axis at magnitude $\left(\frac{nR}{V}\right)$, since $\frac{p}{T}$ remains constant.


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A straight line parallel to temperature axis. 


It will be of the form $y = c$, where $c$ is a constant, mathematically.


Also if you take any value of $\frac{p}{T}$ it will always give same value, because $\frac{nR}{V}$ is a constant.


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