I need to find out how much water to add (in milliliters) to a sealed test tube (which has a volume of 53 milliliters) to achieve a relative humidity of 60% when the temperature is heated 80 degrees Celsius. The 80 degrees Celsius will be achieved in an oven used for Oddy tests. Oddy tests achieve an RH of 100% in the same test tube size listed above by adding 0.4 mL of water and heated to 60 degrees Celsius. The temperature of the room that this will be conducted in (the starting temperature and RH of the test tube when the water is added before it is heated) is about 75 degrees Fahrenheit with an RH of about 20%. I have absolutely no idea what I'm doing and would appreciate any help.
A critical point to add to the previous answer: You must use a saturated salt solution. This means that the maximum amount of salt is dissolved in the water at the temperature of usage - this criterion is only satisfied if there is both solid salt and liquid salt solution present at the same time. Under these conditions the thermodynamics properties are uniquely specified. The system can also tolerate changes in the amount of water in the system. If the humidity is too high some water will condense into the solution (so lowering the humidity) and the solution will dissolve some more salt to maintain saturation. If the humidity is too low water will evaporate from the solution (so increasing the humidity) and the solution will crystallize some some salt. This arrangement is a self correcting stable system. However, for good precision the solution should be mixed and the temperature should be stable.
The referenced article contains extensive information on the properties of a variety of salt solutions and should help you select a suitable salt for your application: https://nvlpubs.nist.gov/nistpubs/jres/81A/jresv81An1p89_A1b.pdf
Other methods, for example using water/glycerin solutions of different compositions, work but do not work well if a significant amount of water evaporates or condenses in the solution while stabilizing humidity.
There is a simple way to do this, as follows.
Salt solutions of different ions often depress the vapor pressure of the water in which they are dissolved. This means that a pan of such a solution will equilibrate with a certain specific water content in the air surrounding it. If the humidity of the air exceeds that which corresponds to equilibrium, the salt solution will pull moisture out of the air, and if the air is drier than that equilibrium, then water will leave the pan.
By selecting a salt that has an equilibrium point near your desired humidity setpoint, you can dissolve it in water, pour it into a pan, and place it in your chamber and it will hold the humidity at the setpoint.
This is a classical problem from physical chemistry, so if you can find a p-chem guru they may be able to help you select the right salt for your application. NOTE! As pointed out by John Matthewson below, be sure to use a saturated salt solution