- #1
Sudarshan_Hebbar
- 17
- 4
How to understand this derivation in a very intuitive way?
Last edited by a moderator:
High School Intuitive Explanation of Adiabatic Condition
- Thread starter Sudarshan_Hebbar
- Start date
Click For Summary
Understanding the derivation of the ideal gas behavior involves concepts like conservation of energy, the ideal gas law, specific heat definitions, and differential equations. The discussion highlights confusion around the differential equation that describes pressure changes during small volume changes in an adiabatic system. The correct formulation of the equation is crucial, as it connects changes in pressure and volume. The participants seek a more intuitive grasp of how these elements interrelate, particularly in the context of the ideal gas behavior. Clarity on these mathematical relationships is essential for a deeper understanding.
How to understand this derivation in a very intuitive way?
- #2
hutchphd
Science Advisor
Homework Helper
- 6,949
- 6,033
As I recall the Feynman Lectures have some usefull discussions for ideal gas.
- #3
Dale
Mentor
- 36,585
- 15,381
Which part are you finding unintuitive?
It is basically the conservation of energy, the ideal gas law, the definitions of specific heat, and a bunch of math. So is it the laws, the definitions, or the math?
It is basically the conservation of energy, the ideal gas law, the definitions of specific heat, and a bunch of math. So is it the laws, the definitions, or the math?
- #4
Sudarshan_Hebbar
- 17
- 4
Mainly, The differential equation. I imagine that it Is describing the process of a small volume change in an adiabatic system and how the pressure is changing in accordance withDale said:
1. the increase in internal energy due to work done by the gas.
2. The change in Volume.
How can I connect these two outcomes to the diffential equation?
- #5
- 23,709
- 5,927
The equation ##\Delta (PV)=P\Delta V+V\Delta P## is incorrect. It should read d(PV)=PdV+VdP. $$\Delta (PV)=P_2V_2-P_1V_1=\left(\frac{P_1+P_2}{2}\right)\Delta V+\left(\frac{V_1+V_2}{2}\right)\Delta P$$Sudarshan_Hebbar said:
- #6
Herman Trivilino
Science Advisor
Gold Member
- 3,755
- 1,769
Sudarshan_Hebbar said:
It's relates dP to dV.
Sudarshan_Hebbar said:
I would just end that sentence there.
Plotted is the Irradiance over Wavelength.
Please check for logarithmic scaling.
As you can see, there are 4 curves.
Blue AM 0 as measured
yellow Planck for 5777 K
green Planck for, 5777 K after free space expansion
red Planck for 1.000.000 K
To me the idea of a gamma-Ray-source on earth, below the magnetic field, which protects life on earth from solar radiation, in an intensity, which is way way way outer hand, makes no sense to me. If they really get these high temperatures realized in...
Similar threads
- · Replies 22 ·
- · Replies 2 ·
- · Replies 5 ·
- · Replies 48 ·
- · Replies 1 ·
- · Replies 6 ·
- · Replies 18 ·