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\subsection{The radiation on a very nice day}
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\subsubsection{The phenomenon}
%
Especially after a year's hot summer every car driver 
knows a sort of a glass house or greenhouse effect: 
If he parks his normally tempered car in the morning 
and the Sun shines into the interior of the car
until he gets back into it at noon, 
he will almost burn his fingers at the steering wheel, if the 
dashboard area had been subject to direct Sun radiation. 
Furthermore, the air inside the car is unbearably hot, 
even if it is quite nice outside. One opens the window 
and the slide roof, but unpleasant hot air may still 
hit one from the dashboard while driving. One can notice 
a similar effect in the winter, only then one will probably 
welcome the fact that it is warmer inside the car than outside. 
In greenhouses or glass houses this effect is put to use: 
the ecologically friendly solar energy, for which 
no energy taxes are probably going to be levied 
even in the distant future, is used for heating. 
Nevertheless, glass houses have not replaced conventional 
buildings in our temperate climate zone not only because 
most people prefer 
to pay energy taxes, 
to heat in the winter,
and 
to live in a cooler apartment on summer days, 
but because glass houses have other disadvantages as well.
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\subsubsection{The sunshine}
%
One does not need to be an expert in physics 
to explain immediately why the car is so hot inside: 
It is the Sun, which has heated the car inside like this. 
However, it is a bit harder to answer the question why 
it is not as hot outside the car, although there 
the Sun shines onto the ground without obstacles. 
Undergraduate students with their standard physical 
recipes at hand can easily \lq\lq explain\rq\rq\ 
this kind of a greenhouse effect: 
The main part of the Sun's radiation 
(Figure~\ref{Fig:nb002nb003})
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\input{GerlichTscheuschner2007a_230_real_greenhouses_radiation_spectra_fig_nb002nb003_} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
passes 
through the glass, as the maximum 
(Figure~\ref{Fig:nb012nb013})
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\input{GerlichTscheuschner2007a_230_real_greenhouses_radiation_spectra_fig_nb012nb013_} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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of the solar radiation is of bluegreen wavelength
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\begin{equation}
\lambda_{\mbox{\scriptsize\rm bluegreen}} = 0.5\ \mu{\rm m}
\end{equation}
% 
which the glass lets through. This part can be 
calculated with the Kirchhoff-Planck-function.

Evidently, the result depends on the type of glass. 
For instance, if it is transparent to electromagnetic
radiation in the 
$300\,{\rm nm}$\,-\,$1000\,{\rm nm}$ 
range 
one will have
%
\begin{equation}
\frac{ \int_{0.3\,\mu{\rm m}}^{1\,\mu{\rm m}} {\rm B}_\lambda^{\mbox{\scriptsize\rm sunshine}} (5780)\,d\lambda }
     { \int_0^\infty {\rm B}_\lambda^{\mbox{\scriptsize\rm sunshine}} (5780)\,d\lambda }
= 77,2\,\%
\end{equation}
%
In case of a glass, 
which is assumed to be transparent
only to visible light
($380\,{\rm nm}$\,-\,$760\,{\rm nm}$) 
one gets
%
\begin{equation}
\frac{ \int_{0.380\,\mu{\rm m}}^{0.760\,\mu{\rm m}} {\rm B}_\lambda^{\mbox{\scriptsize\rm sunshine}} (5780)\,d\lambda }
     { \int_0^\infty {\rm B}_\lambda^{\mbox{\scriptsize\rm sunshine}} (5780)\,d\lambda }
= 44,8\,\%
\end{equation}
%
Because of the Fresnel reflection\TschSpace%
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\cite{Jackson1962}
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%
at both pane boundaries 
one has to subtract 
$8$\,-\,$10$ percent
and only 
$60$\,-\,$70$ percent 
(resp.\ $40$ percent)  
of the solar radiation 
reach the interior of the vehicle.
High performance tinted glass which is also referred to 
as \textit{spectrally selective tinted glass} reduces 
solar heat gain typically by a factor of $0.50$ 
(only by a factor of $0.69$ in the visible range) 
compared to standard glass\TschSpace%
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\cite{EfficientWindowsOrg}.
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\subsubsection{The radiation of the ground}
%
The bottom of a glass house has 
a temperature of approximately $290\,{\rm K}$
(Figure~\ref{Fig:nb004nb005}). 
The maximum of a black body's radiation
can be calculated with the help of Wien's 
displacement law
(cf.\ Figure~\ref{Fig:nb016nb017nb018nb019} 
      and Figure~\ref{Fig:nb021})  
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\input{GerlichTscheuschner2007a_230_real_greenhouses_radiation_spectra_fig_nb004nb005_}%%%%%%%%%T%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\input{GerlichTscheuschner2007a_230_real_greenhouses_radiation_spectra_fig_nb014nb015nb016nb017_}%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\input{GerlichTscheuschner2007a_230_real_greenhouses_radiation_spectra_fig_nb021_}%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\begin{equation}
\lambda_{\mbox{\scriptsize\rm max}}(T) \cdot T = {\rm const.}
\end{equation}
%
giving 
%
\begin{equation}
\lambda_{\mbox{\scriptsize\rm max}}(300\,{\rm K})
=
\frac{6000\,{\rm K}}{300\,{\rm K}}
\cdot
\lambda_{\mbox{\scriptsize\rm max}}(6000\,{\rm K})
=
10\,\mu{\rm m}
\end{equation}
%
This is far within the infrared wave range, 
where glass reflects practically all light, 
according to Beer's formula\TschSpace%
%
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\cite{Weizel1963}.
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% 
Practically 100 percent of a black body's radiation 
at ground temperatures lie above the wavelengths 
of 3.5 $\mu{\rm m}$. 
The thermal radiation of the ground is thus 
\lq \lq trapped\rq\rq\ by the panes. 
 
According to Wien's power law 
describing the intensity of the maximum wave-length
%
\begin{equation}
{\rm B}_{\lambda_{\mbox{\scriptsize\rm max}}} (T) \propto T^5
\end{equation}
%
the intensity of the radiation 
on the ground at the maximum is
%
\begin{equation}
\frac{T^5_{\rm Sun}}{T^5_{\mbox{\scriptsize\rm Earth's ground}}} 
\approx
\frac{6000^5}{300^5} 
=
20^5
= 
3.2 \cdot 10^6
\end{equation}
%
times smaller than on the Sun and
%
\begin{equation}
\frac{T^5_{\rm Sun}}{T^5_{\mbox{\scriptsize\rm Earth's ground}}} 
\cdot
\frac{{\rm R}^2_{\mbox{\scriptsize\rm Sun}}}
     {{\rm R}^2_{\mbox{\scriptsize\rm Earth's orbit}}}
\approx
20^5
\cdot
\frac{1}{215^2}
\approx
70
\end{equation}
%
times smaller than the solar radiation on Earth.

The \textit{total radiation} can be calculated 
from the Stefan-Boltzmann law
%
\begin{equation}
{\rm B}_{\mbox{\scriptsize\rm total}} (T) = \sigma \cdot T^4
\end{equation}
%
Hence, the ratio of the intensities
of the sunshine and the ground radiation
is given by
%
\begin{equation}
\frac{T^4_{\rm Sun}}{T^4_{\mbox{\scriptsize\rm Earth's ground}}} 
\cdot
\frac{{\rm R}^2_{\mbox{\scriptsize\rm Sun}}}
     {{\rm R}^2_{\mbox{\scriptsize\rm Earth's orbit}}}
\approx
20^4
\cdot
\frac{1}{215^2}
\approx 3.46
\end{equation}
%
Loosely speaking, the radiation
of the ground is about four times weaker 
than the incoming solar radiation. 
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%
\subsubsection{Sunshine versus ground radiation}
%
To make these differences even clearer, 
it is convenient to graphically represent 
the spectral distribution of intensity 
at the Earth's orbit and of a black radiator 
of $290\,{\rm K}$, respectively, 
in relation to the wavelength.
(Figures \ref{Fig:nb006nb007}, \ref{Fig:nb008nb009}, and \ref{Fig:nb010nb011})
%
\input{GerlichTscheuschner2007a_230_real_greenhouses_radiation_spectra_fig_nb006nb007_} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\input{GerlichTscheuschner2007a_230_real_greenhouses_radiation_spectra_fig_nb008nb009_} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\input{GerlichTscheuschner2007a_230_real_greenhouses_radiation_spectra_fig_nb010nb011_} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
To fit both curves into one drawing,
one makes use of the technique of super-elevation
and/or applies an appropriate re-scaling.
It becomes clearly visible, 
%
\begin{itemize}
\item that the maxima are at 
      0.5 $\mu{\rm m}$ 
      or 
      10 $\mu{\rm m}$, 
      respectively; 
\item that
      the intensities of the maxima 
      differ by more than an order 
      of ten; 
\item that above 0.8 $\mu{\rm m}$   
      (infrared) the solar luminosity 
      has a notable intensity.
\end{itemize}
%
Figure~\ref{Fig:nb010nb011} 
is an obscene picture,
since it is physically misleading.
The obscenity will not remain in the eye of the beholder,
if the latter takes a look at the obscure scaling factors
already applied by Bakan and Raschke in an undocumented 
way in their paper on the so-called natural greenhouse effect\TschSpace%
%
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\cite{Bakan2002}.  
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%
This is scientific misconduct as is the missing citation. 
Bakan and Raschke borrowed this figure from  
%
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\ifthenelse{\equal{IJMPB}{\TschStyle}}
           {Ref.~\refcite{Luther1985}}
           {}%
\ifthenelse{\equal{arXiv}{\TschStyle}}
           {Ref.~\cite{Luther1985}}
           {}% 
\ifthenelse{\equal{TeX4ht}{\TschStyle}}
           {Ref.~\cite{Luther1985}}
           {} 
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%
where the scaling factors,
which are of utmost importance 
for the whole discussion, 
are left unspecified. 
This is scientific misconduct as well.  
%
\subsubsection{Conclusion}
% 
Though in most cases the preceding 
\lq\lq explanation\rq\rq\ 
suffices to provide an accepted solution 
to the standard problem,
presented in the undergraduate course,
the analysis leaves the main question untouched, 
namely, why the air inside the car is warmer 
than outside and why the dashboard is hotter 
than the ground outside the car. 
Therefore, in the following, the situation 
inside the car is approached experimentally.
% 
