I need a mathematical genius

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try googling for the volume of an irregular object...

 

There is no formula for the space inside a car.

Best way is sucessively approximation using standard solids, or build it up from elemental solids.

Do seats represent air, or not? If not, most seats these days are a very complicated shape, so this will need further work.

How accurate do you want this?

Harry.

 

ok what you trying to do here exactly?

 

If it were for a car interior you could find the spec from the appropriate manufacturer but if it isn't you would need to find someone good at maths;




Si

 

Ejectable seat, so when her boyfriend gets on her nerves, she just press the button, and away he goes...

 

I think you would need to fill the interior of the car up with water or some other similar liquid and then drain that liquid into a suitable container where you could then measure it's volume

Eureka

 

Hm - so you'll need much more than just the internal volume of the car! Like the thermal conductivity of the materials of the car, and the ambient temperature assumed for outside the car.

And are there any occupants? Body heat will be needed to be factored in if so....

Harry.

 

Yup. Assume the car is made of a perfect insulator. Then if you heat the car to 20°C above the outside temperature there will be no loss, so no further heating is required to maintain this differential.

But cars *aren't* made of such materials, so to *maintain* it at that differential will be directly related to the losses through the material of the car.

Harry.

 

Arroryn,

Is this for a particular car or any car in general?

 

Arroryn,

It sounds like we're on the same first step of trying to determine the volume of air contained on the inside of the car. Here's the "simple verbal" equation to calculate the interior volume.

Interior air volume = Volume of the exterior skin of the entire vehicle - volume of all components of the vehicle (including the volume of the sheet metal used in the body).

This is like getting a 1L container and filling it up with water. Then, physical items like the car seats, the steering wheel, and the accelerator/brake pedals are like putting solid objects into te 1L container full of water like marbles. Therefore, the remaining water in the 1L container equals the volume of the interior.

Now, you're going to have to assume this car is somehow airtight, watertight, and thermally insulated from the outside. That's because in general, as the temperature of a gas increases, the volume of the air attempts to expand. For a non-airtight vehicle, the expanding air will leak out of say the edges of the car door. But if it was airtight, then instead of expanding of volume, the pressure of the gas will increase instead. However, that increase in pressure may lead to increase of the temperature of the interior air. The car is also required to be thermally insulated from the environment because that is where energy loss can occur, which would result in the requirement of more energy to maintain the same ambient temperature.

Now, since we're talking about a real car, we need to take into account the environmental temperature. This is because without any attempt at raising or lowering the interior temperature, the First Law of Thermodynamics dictates that the interior temperature will equal the exterior temperature. So let's say the temperature outside is 30 degrees Celcius, then allowing enough time for the interior of the car to reach thermal equilibrium, the interior will also become 30 degrees Celcius. What that means is, there is no additional energy required to maintain that 30 degrees Celcius inside. However, energy will be required to RAISE the interior temperature relative to exterior temperature by a heater. Ironically, it's going to also require additional energy to LOWER the interior temperature relative to exterior temperature by the air conditioner.

As other previous posters have mentioned, this problem becomes more complicated if there's a driver who's respirating. That's because in that case, you do not want an airtight car or else your driver will no longer be respirating. First, due to the presence of the driver will be a factor that will decrease the volume of air inside the car. Second, during the decay process, more and more carbon dioxide will be released, which would make the problem more complicated due to consideration of partial pressures of the nitrogen, oxygen, carbon dioxide, and other trace gasses present inside the car.

So in summary, this problem can get extremely complicated unless you give us more information that may constrain the problem in certain ways. In other words, it would help to know why you're asking this question.

 

That is Caroyl Vouderman, a maths genuis.

Si

Edit;

As for keeping the car and a consistant temperature, you need Air conditioning with Climate control!

 

Its not underwear is it?

 

Mabe it's for keeping the beer cool!
http://www.outdoorgb.com/c/portable_fridges/

what about:-

'Vacuum Casting'
or Resign Casting - things will get a bit messy here!



otherwise :- read this to find out how air con works inside a car:-

http://www.fordscorpio.co.uk/aircon.htm

 

Once you've worked out the volume of air in the car, you need to start looking at specific heat capacity. SHC is basically the ratio of proportionality of change in temperature and the energy required to effect that change in temperature.
If you wanted to change the temperature of a volume of air the equation is:

Energy = (change in temp.) x SHC x (mass - calculated fromt he volume).

amd the specific heat capacity of air is (almost) 1.

Once the air is at the required temperature, you'd need to think about keeping it there, this is a little trickier. If this was thermostat controlled, say the cooling/heating element came on at +/- 1 degree of the target temperature, you would need to know the time it would take for that temperature change of one degree, using the specific heat capacity equation, you can work out how much energy is used in cooling/heating the air back to the target temperature and then work out how many times this happened over a certain time (say a day). Of course, this is assuming a 100% efficient element and if you have one of those, then congratulations, you've just performed the physicist's equivalent of turning lead into gold!

In short, you're opening up a whole can of worms!

 

Arroryn,

Here's the general equation to find the volume of a rectagular cuboid...

Volume = Length x Width x Depth

Now, if you specify the lenth to be 10 m , specify the width to be 10 m, and specify the depth to be 10 m, you can calculate the specific answer that is...

Volume = 10 m x 10 x 10 m
Volume = 1000 m ^ 3

The point being, unless you start specifying certain factors about this problem, e.g. "length is 100 m", the "answer" to your problem may remain as a generalized differential equation with many variables and no closer to your requirement of specifically determining the "specific amount of energy required to maintain a specific temperature." You stated you have some experience with calculus. This is in the world of integral calculus. So even with an extremely simple equation of "10" you have...

Code:

If...

f'(x) = 10

Then...

       S
f(x) = S 10 dx
       S 

f(x) = 10x

That is an infinite amount from 0 to infinity, or even -infinity to infinity. But if you specify "x = 10", then you can find the specific answer of f(x) = 10(10) = 100.

So the irony is, the less you specify, the more complicated the problem becomes.