# Relationship between pressure and temperature adiabatic

### PV diagrams - part 2: Isothermal, isometric, adiabatic processes (video) | Khan Academy The ratio of the specific heats γ = CP/CV is a factor in determining the speed of sound With the initial volume and temperature specified, the initial pressure is. Mar 11, When an ideal gas is compressed adiabatically, work is done on it and its The temperature, pressure, and volume of the resulting gas-air. The translation kinetic energy of the particles is related to the temperature by that the pressure and volume of an ideal gas obey the equation (called the .. heats, it can be shown that, in an adiabatic process, an ideal gas obeys the relation.

Water doesn't change its temperature very easily since it has such a high specific heat, so if the tank is very large, this water's gonna maintain the same temperature, it's not gonna care about a little piston in here, but the gas in the piston is gonna try to maintain equilibrium with temperature of the water. So if you make this process happen very slow, if I push down the piston very slow, I'll add energy, but that energy's gonna get taken out, the temperature of the gas will remain the same if I do it slow enough, or I can pull up on the piston very slowly, then some heat has to enter into the gas so that it always maintains the same temperature with the outside environment, ensuring that it's an isothermal process.

So what's an isothermal process look like on a PV diagram? Well, let's look at the Ideal Gas Law. N number of molecules in here, that's a constant we're not letting any gas molecules in or out. K, that's Boltzmann's Constant, that number doesn't change. For an isothermal process, temperature's also a constant. So the actual shape of the line drawn on a PV diagram for an isothermal process is sometimes called an isotherm and they look like that.

Remember, that's how we found the work done by the gas in an isobaric process, but that was because we had a nice rectangle. The area underneath this graph is still gonna give us the work done, that's true.

This definitely is the work done by the gas, but it's not a perfect rectangle so you can't use this formula, you'll have to know, you'll have to be given the heat and then you can figure out the work or given the work, you'll find the heat.

There's not a really good way, unless you're gonna do calculus, to figure out the area underneath this curve. One more thing that you should definitely know. Because the NKT is a constant, right, all of this stuff is not changing for an isothermal process, that means P x V is also not changing. That's another thing that doesn't change. So T doesn't change, U, the internal energy, doesn't change, and P x V does not change as well because T isn't changing over here in the Ideal Gas Law. That means, if you take the pressure times the volume at any point along this isotherm, you'll get the same number so this volume here and this pressure right here, if I take those two and I multiply those two together, I'll get some number, and if I take the final one, this volume and this pressure, and I multiply those two numbers, I'll get the same number.

I'll get the same result for P x V. I'll get the same result here, if I take these two, any P x V value along this line is gonna be the same because that number can't change, cause if it did that'd mean the temperature had to be changing and then you wouldn't have an isotherm.

So that's the isothermal process. That's one of the four most common thermal processes. We've got two more to go. Let's talk about the isometric process. The first thing you should know is this is sometimes called isochoric, and it's also sometimes called isovolumetric.

Why does it have three names? I don't know, but they all mean the same thing. Iso means constant, volumetric and choric and metric all refer to size or volume This means constant volume.

## 3.6: Adiabatic Processes for an Ideal Gas

How do you make sure that happens? Well, just don't let the piston move. The piston is the thing that regulates the volume. Well, that thing's shut, I dunno, keep that thing from moving and you'll have, no matter what else happens, an isometric, isochoric, or isovolumetric process, which all mean the same thing. Now, since the piston can't move, that means no work can be done.

The gas can't do any work, the outside forces can't do any work, you can't do any work on the gas. No work can be done if this piston cannot be moved up or down. So W's always going to equal 0 for one of these isometric processes. So these isometric processes are actually pretty simple. What do they look like on a PV diagram? Well, the volume is staying constant. Pressure staying constant is a horizontal line, so volume staying constant is a vertical line.

And if I add heat, I'll increase the pressure, and if I take heat away, I'll decrease the pressure, and this volume will remain the same, cause this piston is not allowed to move.

Now remember that work is the area underneath the curve. Does that make sense over here? How much area is underneath this curve? There's no area underneath this curve. There's no area, you've just got this line here, that's not an area, that's infinitesimally thin and so that means there's no area, no area means no work is done, and that agrees with what we know about an isometric process All right, one more of the big four processes to go.

### Isothermal and adiabatic expansion

This is one in which no heat is exchanged, so sometimes people hear that and they think, "Oh, that means that there's no change "in the temperature, right? This is definitely not what we're saying. No heat exchanged means that Q, our letter that we use to represent the heat, is 0. It means that no heat is allowed into the gas, no heat is allowed to flow out of the gas. These do not happen for an adiabatic process. And that does not mean that the temperature can't change. The temperature can change here because the piston can do work or the work can be done by the gas, but no heat can flow in or out.

So you've gotta get good at delineating between the temperature and the heat. In contrast, free expansion is an isothermal process for an ideal gas. Adiabatic heating occurs when the pressure of a gas is increased from work done on it by its surroundings, e. This finds practical application in diesel engines which rely on the lack of heat dissipation during the compression stroke to elevate the fuel vapor temperature sufficiently to ignite it.

Adiabatic heating occurs in the Earth's atmosphere when an air mass descends, for example, in a katabatic windFoehn windor chinook wind flowing downhill over a mountain range. When a parcel of air descends, the pressure on the parcel increases. Due to this increase in pressure, the parcel's volume decreases and its temperature increases as work is done on the parcel of air, thus increasing its internal energy, which manifests itself by a rise in the temperature of that mass of air.

The parcel of air can only slowly dissipate the energy by conduction or radiation heatand to a first approximation it can be considered adiabatically isolated and the process an adiabatic process. Adiabatic cooling occurs when the pressure on an adiabatically isolated system is decreased, allowing it to expand, thus causing it to do work on its surroundings. When the pressure applied on a parcel of air is reduced, the air in the parcel is allowed to expand; as the volume increases, the temperature falls as its internal energy decreases.

Adiabatic cooling occurs in the Earth's atmosphere with orographic lifting and lee wavesand this can form pileus or lenticular clouds. Adiabatic cooling does not have to involve a fluid.

## PV diagrams - part 2: Isothermal, isometric, adiabatic processes

One technique used to reach very low temperatures thousandths and even millionths of a degree above absolute zero is via adiabatic demagnetisationwhere the change in magnetic field on a magnetic material is used to provide adiabatic cooling.

Also, the contents of an expanding universe can be described to first order as an adiabatically cooling fluid. See heat death of the universe. Rising magma also undergoes adiabatic cooling before eruption, particularly significant in the case of magmas that rise quickly from great depths such as kimberlites.

13. Thermodynamics - Proof of Adiabatic Equation - Most Important

In practice, no process is truly adiabatic. Many processes rely on a large difference in time scales of the process of interest and the rate of heat dissipation across a system boundary, and thus are approximated by using an adiabatic assumption. There is always some heat loss, as no perfect insulators exist. Ideal gas reversible process [ edit ] Main article: Reversible adiabatic process For a simple substance, during an adiabatic process in which the volume increases, the internal energy of the working substance must decrease The mathematical equation for an ideal gas undergoing a reversible i.