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There might be an obvious reason for this, but yesterday, while travelling in the bus, it was heavily raining outside and the window panes becomes frosty and hazy so I could write a bunch of stuff on it. Why does this happen?

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That is because water had condensed onto the window pane. This water on the window pane condensed out of air. Prior to condensation, it was in the form of vapor. Now for a given water vapor pressure in air, condensation into liquid water can only occur if the temperature drops sufficiently low (to be precise, lower than saturation temperature). So rain must have cooled the window pane sufficiently for this to happen. Either that or rain increased the water vapor content of the air enough to make the corresponding saturation temperature exceed the temperature of the window pane.

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Where I live, the rain from Cumulonimbus storms is usually colder than the surface air (sometimes it comes down as hail). This can cool the window glass so that water condenses on the inside.

I don't know whether this applies in other situations such as tropical monsoons.

Perhaps someone can provide a basic physical reason why rain should be colder.

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