|MadSci Network: Physics|
Well, ordinarily the concept of 'specific heat' does not refer to 'volume'; it is merely the amount of energy it takes to raise the temperature of one gram of (pick a substance) by one degree Celsius.
Your question seems reasonable in the light of the well-known fact that a gas tends to expand when its temperature rises. Also, if such expansion is allowed to occur, an accompanying drop in temperature will affect the final amount of expansion. Obviously, to be able to measure the correct rise in temperature of a gas as energy is applied, it is necessary to confine it to a fixed volume.
I am sorry, but I do not know if there is a "standard apparatus" for making this measurement. It seems to me simple enough for any student to compute the volume of one gram of gas, and for any good workshop to build an insulated and sealable container of that size. Prior to using the apparatus on a gas, it would be necessary to test it out in a vacuum chamber, to find out how much energy raises ITS temperature by one degree. (It is necessary to discover an energy/temperature/time relationship, since the aforementioned insulation would warm more slowly than the interior walls of the apparatus.)
Once the background data are known, the container can be injected with the requisite single gram of gas, and heated. Gases being good conductors of heat via the convection effect, one should be able to quickly discover a new energy/temperature/time relationship. When the background data are subtracted out, the specific heat of the gas would then be known.
The first person to have constructed such an apparatus would likely have tested many different gases, and published the results. A few others would have built their own apparatus to verify or challenge the results. After an early flurry of such testing, the subject probably remained relatively ignored -- if the data can be found in the literature, then it has probably been proven reliable enough for most needs. There are only so many different gases, after all. The existence of a "standard apparatus" would imply a great need for constant testing and verification. I don't know of any such need; do you? And while I can understand a desire to obtain more accurate mesurements, it is quite obvious that no "standard apparatus" would be up to that task!
In summation, whether or not there really is a standard apparatus for measuring the specific heat of gases, I hope I have at least answered your question about how it could be done.
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