Adiabatic Expansion - proof of PV^(gamma) = constant

In summary, adiabatic expansion is a process in which a gas expands without any heat transfer. The proof of PV^(gamma) = constant for adiabatic expansion is based on the first law of thermodynamics and the relationship between pressure, volume, and the adiabatic constant gamma (γ). The adiabatic constant is determined by the ratio of specific heats, and the proof makes several assumptions. This proof is used in practical applications such as designing heat engines and calculating work done by a gas during an adiabatic expansion.
  • #1
CAF123
Gold Member
2,948
88
Hi,

I was looking at the proof for the derivation of the condition satisfied by adiabatic processes. (The proof can be found in many introductory physics textbooks, I am using Principles of Physics HRW 9th ed.) At some point , they say 'For an ideal gas PV=nRT and if P,V T are allowed to take on small variations we have that PdV + VdP = nRdT'. Where does the part in bold come from, specifically the PdV +VdP?

Sorry if I have overlooked something obvious.
 
Physics news on Phys.org
  • #2
The derivative of product of variables. d(PV)=VdP +PdV
 

1. What is adiabatic expansion?

Adiabatic expansion refers to the process in which a gas expands without any heat transfer between the gas and its surroundings. This means that the gas experiences a change in volume and pressure, but its temperature remains constant.

2. What is the proof of PV^(gamma) = constant for adiabatic expansion?

The proof of PV^(gamma) = constant for adiabatic expansion is based on the first law of thermodynamics, which states that the change in internal energy of a closed system is equal to the heat added to the system minus the work done by the system. By applying this law to an adiabatic expansion process, we can derive the relationship between pressure, volume, and the adiabatic constant gamma (γ).

3. How is the adiabatic constant gamma (γ) determined?

The adiabatic constant gamma (γ) is determined by the ratio of specific heats, which is the ratio of the amount of heat required to raise the temperature of a gas at constant pressure to the amount of heat required to raise the temperature of the gas at constant volume. For an ideal gas, the value of gamma is always greater than 1.

4. What are the assumptions made in the proof of PV^(gamma) = constant?

The proof of PV^(gamma) = constant for adiabatic expansion makes the following assumptions: 1) the gas is in a closed system, 2) the gas is behaving ideally, 3) there is no heat transfer during the expansion, and 4) the expansion is reversible.

5. How is the proof of PV^(gamma) = constant used in practical applications?

The proof of PV^(gamma) = constant is used in various practical applications, such as in the design of heat engines and gas turbines. It is also used to calculate the work done by a gas during an adiabatic expansion, and to analyze the efficiency of gas compression and expansion processes.

Similar threads

I Graphical difference between adiabatic and isothermal processes.
    • Thermodynamics
Replies
1
Views
637
I Solving Adiabatic Process for Two Compartments
    • Classical Physics
Replies
1
Views
916
I Does the Euler method give a better insight into adiabatic processess?
    • Classical Physics
Replies
6
Views
810
Adiabatic expansion with temperature-dependent gamma
    • Introductory Physics Homework Help
Replies
1
Views
827
I Description of Adiabatic Expansion
    • Other Physics Topics
Replies
8
Views
1K
Thermodynamics - Enthelpy change in adiabatic expansion
    • Engineering and Comp Sci Homework Help
Replies
3
Views
3K
Ideal Gases under Adiabatic Compression
    • Classical Physics
Replies
2
Views
3K
Show that ##pV^\gamma## is a constant for an adiabatic process
    • Advanced Physics Homework Help
Replies
4
Views
1K
Finding work of adiabatic compressor using ideal gas
    • Engineering and Comp Sci Homework Help
Replies
4
Views
3K
Reversible adiabatic expansion -- calculate change in E
    • Advanced Physics Homework Help
Replies
8
Views
2K

Hot Threads

Recent Insights

Back
Top