density, temperature and pressure
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That depends what aspect of the gas you want to measure: its volume, its pressure, its temperature, its density, etc.
That depends upon the volume of the object that is put into the water in the bathtub.
Depends upon the density of the subject (microgram is a unit of mass, mililitre is a unit of volume).
That depends upon the temperature, pressure, and type of gas. For more information, study the ideal gas law. One form of the ideal gas law is PV=nRT, where P=pressure, V=volume, n=number of moles of gas, R=0.08206 L-Atm-mol-1-K-1, T=temperature in degrees K. By rearranging this equation, you could calculate the number of moles of gas if you knew the volume, temperature, and pressure of the gas. Then multiply by the molecular weight of the gas to get the grams, and divide by 1000 to get kilograms.