Originally, I simply wanted a way to plot $ \ln(T^{3/2})$ versus $ \dfrac{1}{k_B T}$

But all that appeared was this:

`In[20]:=Plot[ln[T^{3/2}], 1/{1.38 10^{-23} T} {T, 0, 10}, PlotLabels -> "Expressions"] Thread::tdlen: Objects of unequal length in {{7.24638*10^22/T}} {T,0,10} cannot be combined. Plot::pllim: Range specification {T,0,10}/{1.38 10^{-23} T} is not of the form {x, xmin, xmax}. `

So, I’m trying to plot a graph of $ $ y=\ln(T^{3/2})$ $ and $ $ y=\frac{1}{k_B T}$ $ , where $ k_B\approx 1.38 \times 10^{-23}$ and is the Boltzmann constant. $ T$ is the thermodynamic (absolute) temperature.

`In[17]:= Plot[y = ln (T^{3/2}), y = frac {1} {1.38 10^{-23} T}, {T, 0.0001, 1000}, {y, 0, 100000} PlotLabels -> "Expressions"] Plot::nonopt: Options expected (instead of {y,0,100000} PlotLabels->Expressions) beyond position 2 in Plot[y=ln T^{3/2},y=frac {1} {1.38 10^{-23} T}, {T,0.0001,1000},{y,0,100000} PlotLabels->Expressions]. An option must be a rule or a list of rules. Out[17]=Plot[y = ln \!\(\*SuperscriptBox[\(T\), \({\*FractionBox[\(3\), \(2\)]}\)]\), y = frac {1} {1.38 \!\(\*SuperscriptBox[\(10\), \({\(-23\)}\)]\) T}, {T, 0.0001, 1000}, {y, 0, 100000} PlotLabels -> "Expressions"] `

I’m really stuck and don’t know what to do, I would prefer if the first method (by not letting $ y=…$ ) would work but since it didn’t I tried the second way and that didn’t either.

Any hints or tips will be appreciated.