Heating the Gloriette in Schönbrunn Palace Garden?

The year of 2011 was very eventful for me. In the beginning of the year I got pregnant. Then I managed to organize a big wedding. And finally we are on our honey moon in beautiful Prague and noteworthy  Vienna. As we were joking, it turn to be neither honey,  neither moon, but more like a week in walking, sightseeing and friends.

On our last day we visited the Schonbrunn palace outside Vienna. We decided to go for the tour with a small train around the whole complex. After having a lunch we strolled to the Gloriette  situated on a hill overlooking the magnificent garden, the palace, and the city. . As we entered the building we were amazed by the volume and the architecture inside. We found an cafe in it. As luck might have it a table on a big panoramic window was just being freed. So we sat there.

One might thing that at this romantic moment on our honey moon we might be discussing how happy we are, and how we will love each other for eternity. But… the conversation turned entirely other direction – as we were looking the big volume of the saloon – we started to wonder how much energy would it take to heat this room in the winter. As it turns out the solution was not very easy to come up with, so we had to wait till the evening to ask uncle Google for a little help.

Before the math part, let's have a look at the building itself!

The Gloriette

"Gloriette" is a french word from 12th century meaning "little lady".  Today it's a noun that refers to a building in a palace garden. It is usually erected on a hill, thus having a panoramic view to the surroundings. Its shape varies a lot, but often it's reminiscent of ancient tomb or pavilion (not the one you can get newspapers from, but free-standing structure that is an object of pleasure). The Gloriette we've visited in Vienna is the largest and the most popular!

It was built in 1775 according to the plans of Austrian imperial architect Johann Ferdinand Hetzendorf von Hohenberg. The pavilion was used as a dining hall (for breakfasts of Franz Joseph) and festival hall.

Today, in addition to the cafe, it has an observation platform on the roof. It is a barely know fact that a 10% smaller copy of the Gloriette is situated in skirts of Sanghai, China. That's in short about The Gloriette' architecture.

    

How to heat it

The first thing to consider is the volume of the room. It is easy enough task,  if you happen to know the x, y and z dimensions. Which we did not have. So trusting our eyes only, we decided them to be 20m by 30m and with height of 20m. In total the inner volume of the Gloriette is 12 000 cubic meters. The other thing that we fixed was that the outside temperature to be 0^o C and the target inside temperature to be 22^o C. So the question turned out to be how much energy is needed to heat the 12 000 m³ from 0 to 22 degrees.

As the first step we do not consider heat loses, which would be enormous for such poorly isolated building with large single glazed windows. As a second step we will try to include them also (which will appear in another blog).

To simplify the task, we fix the first step of the solution as: how much energy(Wh) is needed to heat 1 cubic meter of air by 1 degree? We spend some time googling around and trying to remember the basic physical formulas, until we came up with the magic formula :

rQ = c · p · V · rt

                   rQ = ?      – heat, wanted

                   c = 1005 J/kg · ^oC     – specific heat capacity of air for typical room conditions
                   p = 1250 kg/m³       – density of dry air in range from 0 to 20^oC

                   V = 1 m³      – volume of air

                   rt= 1^oC      – temperature change

Doing the substitution, we get the important number (please J let me know if you think the calculation is not correct):

Q = 1005  ·  1250  ·  1  ·  1 = 1256 J = 1256 Ws = 0,3488 Wh

So, we need 0,35 Wh of energy to heat 1 cubic meter of air by 1 degree. Doing the computation further for 0 ^oC  to 22 ^oC and 1200m³ :

0,3488 ·  22  ·  1200 = 92083,2 Wh = 92 kWh

In conclusion, we need 92 kWh of energy to heat air volume of 1 200 m³ by 22 ^oC if there are no heat loses through the walls and windows.

So, as you see, being on a honey moon is not always romantic walks and talks! Each couple with its peculiarities! For us, these brain gymnastics are often a source of real pleasure :-). Adoring great architecture is always emotional act, and sometimes it happens to provoke technical questions, too. In  part 2 we would go further with the  investigation of the heat loses and how to heat the building and what it would cost.