![]() The work done by just saying Work is PΔV. Line drawn on a PV diagram for an isothermal process is sometimes called an isotherm and they look like that. It's gonna curve like 1/x and it can be an isothermalĮxpansion if volume increases or an isothermal compression Isothermal process is gonna look something like this, Y = a constant over x, and we know what 1/x looks Numerator's a constant, and we just have P, as aįunction is constant/V, so P just goes like 1/x. In here, that's a constant we're not letting any P x V = NKT, at least the Boltzmann's Constant version of it does, so I want to know what the pressure is as a function of volume, let Look like on a PV diagram? Well, let's look at the Ideal Gas Law. The outside environment, ensuring that it's an isothermal process. So that it always maintains the same temperature with Very slowly, then some heat has to enter into the gas Same if I do it slow enough, or I can pull up on the piston Taken out, the temperature of the gas will remain the Very slow, I'll add energy, but that energy's gonna get Process happen very slow, if I push down the piston Is gonna try to maintain equilibrium with temperature of the water. It's not gonna care about a little piston in here, but the gas in the piston This water's gonna maintain the same temperature, Temperature very easily since it has such a high specific heat, so if the tank is very large, Put the whole container in a tank of water that has a temperature of, say, 290K, a huge tank of water. Thing in a thermal reservoir, this is how you could actually do it. Constant temperature with what? Well, just stick this whole Time to conduct accordingly and maintain a constant temperature. Process happen very slow, add 1 joule per hour or perĭay, make it as slow as possible so that this heat always has ![]() Out of the container or into the container fast enough, so you've gotta make the Process happen too fast, this heat can't conduct Some time for heat to conduct through a container, and if you make the If you make the process happen too fast, this heat, yanno it takes Has time to conduct out or in accordingly. Push down the piston, or if you're pulling it So how do you do this? Well, just make sure you The same temperature as before, that doesn't count. There can't be a delay, otherwise you'd add this 300 joules, the temperature of the gas would increase, and then the heat wouldĬonduct outta here, you know, at its leisure, it would take some time, and then finally you'd reach Take away has to immediately get added back in. You add has to immediately get taken away, or every bit of energy you The same at every moment during the process. To be truly isothermal, the temperature has to remain Just the initial temperature to equal the final temperature. Is -300 joules, that way 300 joules and -300 joules add up to 0, you've got an isothermal process. Heat to leave the gas, 300 joules of heat would have to leave. Gonna remain constant is for 300 joules of Say, 300 joules of work by pushing this down, youĭo 300 joules of work. So what does that mean? That means that Q + W have to add up to 0. The First Law holds, forĪny thermal process in here, whether it's an isotherm,Īn isobar, any of them, so we can say that ΔU has got to equal Q, which is the heat that flows into a gas, plus W, which is the work done on the gas, and now we know, for an isothermal In the internal energy, so what can we say? Well, let's look at theįirst Law of Thermodynamics. No change in the temperature and there's no change Things are gonna happen,īut they're gonna happen in such a way that there's No thermal, if there's "no change in the temperature at all?" Well, you can, stuff's gonna happen here. Minute, how can you have "a thermal process if there's Process, not only is ΔT=0, but more importantly, in terms of the First Law of Thermodynamics, If the temperature doesn't change, the internal energy doesn't change. And so if the temperature doubles, the internal energy doubles. The internal energy of a gas is not equal to, but it's proportional to, the temperature of a gas. Let me show you one more important thing. Is constant, that means the change in the temperature, that means there is noĬhange in the temperature, so the change in the Or, in other words, T equalsĪ constant, which we could also write, if temperature ![]() This is short for temperature so this is a process where the \( \newcommandx \right )+1\),shown as the orange dashed wave.Talked about isobaric processes This time let's talk about ![]()
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