# Adiabatic Processes for an Ideal Gas

• splitringtail
In summary, the problem is to derive the adiabatic processes for an ideal gas going through a point on the p-V plane, and also in terms of p-T and v-T. The necessary equations to solve this problem are the First Law of Thermodynamics, properties of an ideal gas, and properties of adiabatic processes. The student has successfully derived the transformations for the three processes, but is unsure if they should be plotted on the same graph or on their respective planes. The wording of the question is unclear.
splitringtail

## Homework Statement

The problem is derive the adiabatic processes for an ideal gas going through a point (v,p) on the p-V plane. Also, in terms of p,T and v,T. Draw the curves.

## Homework Equations

First Law of Thermo

Properties of an Ideal Gas

Properties of Adiabatic Processes

## The Attempt at a Solution

I derived the transformations, but I am getting the impression from the wording that I have to draw all three curves on the p-V diagram. Yet, I don't know. I figure I have to plot the other two in their respective planes.

splitringtail said:

## Homework Statement

The problem is derive the adiabatic processes for an ideal gas going through a point (v,p) on the p-V plane. Also, in terms of p,T and v,T. Draw the curves.

## Homework Equations

First Law of Thermo

Properties of an Ideal Gas

Properties of Adiabatic Processes

## The Attempt at a Solution

I derived the transformations, but I am getting the impression from the wording that I have to draw all three curves on the p-V diagram. Yet, I don't know. I figure I have to plot the other two in their respective planes.
The question is not clear. Can you provide the actual wording of the question?

AM

That is the problem wording.

I have to derive you know

$$P V^{gamma} = Constant$$

$$P^{1-gamma} T^{gamma} = Constant$$

$$T V^{gamma-1} = Constant$$

Which I have, from like the 1st Law of Thermodynamics and some empirical facts regarding the internal energy and enthalpy of an ideal gas.

My problem is I am confused whether it is possible to plot them on the same graph. It just talks about a point in the P-V planes. I would think I have to plot each on in their respective plane.

## 1. What is an adiabatic process for an ideal gas?

An adiabatic process for an ideal gas is one in which there is no heat transfer between the gas and its surroundings. This means that the gas is insulated and there is no exchange of energy in the form of heat.

## 2. How does an adiabatic process differ from an isothermal process?

An isothermal process is one in which the temperature of the gas remains constant, while an adiabatic process does not allow for any heat transfer, so the temperature of the gas can change. Additionally, an adiabatic process typically involves a faster change in temperature compared to an isothermal process.

## 3. What is the equation for an adiabatic process for an ideal gas?

The equation for an adiabatic process for an ideal gas is PVγ = constant, where P is the pressure, V is the volume, and γ is the heat capacity ratio of the gas.

## 4. What is the significance of the heat capacity ratio (γ) in an adiabatic process?

The heat capacity ratio (γ) is a measure of how much the temperature of a gas changes in response to a change in pressure. In an adiabatic process, the heat capacity ratio is constant, and it determines the relationship between pressure and volume for an ideal gas.

## 5. What are some real-world applications of adiabatic processes for ideal gases?

Adiabatic processes are commonly used in refrigeration and air conditioning systems to compress and expand gases without any heat transfer, allowing for efficient cooling. They are also used in internal combustion engines, where the rapid compression of air and fuel leads to an increase in temperature and pressure, resulting in the expansion that powers the engine.

• Introductory Physics Homework Help
Replies
4
Views
229
• Introductory Physics Homework Help
Replies
19
Views
1K
• Introductory Physics Homework Help
Replies
3
Views
300
• Introductory Physics Homework Help
Replies
1
Views
951
• Introductory Physics Homework Help
Replies
33
Views
1K
• Introductory Physics Homework Help
Replies
10
Views
1K
• Biology and Chemistry Homework Help
Replies
1
Views
159
• Introductory Physics Homework Help
Replies
2
Views
2K
• Introductory Physics Homework Help
Replies
8
Views
891
• Introductory Physics Homework Help
Replies
2
Views
1K