PV= n R T

Some high school algebra on the gas law equation



Let's solve in terms of T ( temperature): Divide both sides by R times n. This yields this equation, which is equivalent to the Gas Law equation, or I don't know my algebra. That would be T= PxV / nx R ; So what does it all mean, Basil?

Let's use a concept in first semester calculus: Let's have n, which is the number of molecules, get really big. Like infinity big. What does that do to the number? It goes to zero, right? That's because the denominator gets bigger. As the denominator gets bigger, the number gets smaller, right? Again, what does that mean, Basil?

Let's swerve away from that for a moment, and look at it from a common sense viewpoint. If n is the number of molecules, then increasing n also increases the mass. To keep Temperature equal, you'd have to increase pressure times volume. But wait, one can get confused. That's why we need some common sense. You'd need more energy to heat more mass to the same temperature, would you not? It takes more heat to boil two cups of tea than one, right? So it means that to maintain temperature at a constant level, you'd have to add more heat when you increase n, or if you don't, you lose temperature.

Seems rather startling at first, but then you recognize that it is just common sense. More stuff to heat means more energy expended. It takes more heat to heat more stuff. Common sense. Does it make more sense then, that more stuff means that more heat can be stored? Wouldn't it also mean that it takes longer to cool off a lot of stuff, than just a little stuff? Just trying to make sense of this equation...

Some of this discussion wouldn't be scientific, but it does make sense. Or I hope it does. That could explain why Venus gets hot and Mars does not. Or part of why. Venus receives much more solar radiation than Mars. It's atmosphere is much thicker. It may be on the order of 10000 times thicker than Mars. Venus is hot, and Mars is cold. But both have a carbon dioxide dominated atmosphere. Therefore, referring to the equation again, in the comparison between planets, the number of molecules in the Venusian atmosphere is much higher than on Mars. It takes a lot more heat to warm it up, but once it does, it stays hot longer. Harder to cool off, let's say.

The idea I'm trying to get across is that it doesn't matter what kind of gas is in the atmosphere. It matters how much gas ( which also means how much mass of that gas) is in the atmosphere. More energy means higher temperature. It takes a lot more energy to heat up the Venusian atmosphere in the first place. If Mars had a thicker atmosphere, would it be hotter? Maybe. But only because there is a lot more matter there to retain the heat. It isn't because Mars would have a runaway greenhouse effect if it had an atmosphere like Venus.

Mars might even be colder than it is right now! That might "bake your bagels", as Bongino would say. Venus gets warmer than Mars because its blanket is a lot thicker. And tomorrow is Ground hog day. It's pretty cold, so break out those thick blankets.