Air has some mass, and therefore weight. Under normal conditions, air has a mass of a bit more than one kilogram per cubic meter. For comparison, this is a bit over 1/1000 of the mass of water.
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You can increase the air pressure inside the bag by reducing the volume of the bag or adding more air molecules to it. This can be done by squeezing the bag to decrease its volume or blowing air into the bag to increase the number of air molecules present inside.
If you increase the atmospheric pressure, the pressure will also increase. This is because atmospheric pressure is the pressure exerted by the weight of air above a certain point, so increasing the amount of air causes an increase in pressure.
The internal energy of air can be increased by adding heat to it. When heat is added to air, the energy of the air molecules increases, causing them to move faster and have higher kinetic energy. This increase in kinetic energy results in an increase in the internal energy of the air.
Adding a base
In general, steam is water so you're adding water to the air and raising the humidity. The small caveat is that steam is also going to heat the air, so it can hold more moisture. By adding moisture you increase the numerator of the relative humidity term, and by raising the heat you increase the denominator. In the end, the moisture would win and the relative humidity would increase.