Why 1 liter * atm = 101.33 joules ?

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Discussion Overview

The discussion centers around the relationship between pressure, volume, and energy, specifically why 1 liter multiplied by 1 atmosphere equals 101.33 joules. Participants explore the underlying reasoning and constants involved in this equivalence, touching on both theoretical and practical aspects.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • Some participants inquire about the logical reasoning behind the equivalence of 1 liter * atm to 101.33 joules, questioning whether it is a constant or has a deeper explanation.
  • Others suggest that the relationship can be derived from the gas constant values, specifically mentioning the constants 8.31447 J/mol K and 0.08206 L atm/mol K.
  • A participant points out that while the gas constant approach is valid, it shifts the question to why those constants hold true, suggesting a more direct conversion to SI units for clarity.
  • Another participant provides a derivation involving work done by a piston, linking pressure, force, area, and displacement to explain how work relates to pressure and volume.

Areas of Agreement / Disagreement

Participants express varying levels of understanding and approaches to the question, with no consensus reached on a singular explanation for the equivalence of 1 liter * atm to 101.33 joules. Multiple perspectives and methods for deriving the relationship are presented.

Contextual Notes

Some limitations include the dependence on specific constants and the potential for confusion regarding the definitions of pressure and volume in different unit systems. The discussion does not resolve the foundational questions about the constants involved.

Tahira Firdous
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Hi ! I have been searching but i am not able to find out that is there any reason behind , why 1 liter * atm = 101.33 joules ?
 
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Are you asking why it comes out equal to 101.33 Joules, or why a pressure (atm) time a volume (liter) gives an energy (joules)?
 
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Nugatory said:
Are you asking why it comes out equal to 101.33 Joules, or why a pressure (atm) time a volume (liter) gives an energy (joules)?
I am asking that why it is equal to 101.33 joules any logical reason or just a constant ?
 
Daniel Hendriks said:
https://lavelle.chem.ucla.edu/forum/viewtopic.php?t=729

multiply the gas constant 8.31447 J/mol K and then divide by the gas constant 0.08206 L atm/mol K.
1 L atm = 101.33 Joules
Even though this is not wrong, is just shifting the question to why 8.31 J equals 0.082 L*atm.
You could just go directly to change the units for pressure and volume to SI units and get the answer.
## 1 atm =1.01 \times 10^5 N/m^2 ##
## 1L =10^{-3} m^3 ##
So
## 1 atm \times 1L = 101 N \cdot m ## or 101 J
 
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+1

Consider a piston of area A moving in a cylinder with constant pressure...

Work = Force * displacement ... (1)

Pressure = Force/Area
so
Force = Pressure * Area ......(2)

sub for force in (1) gives...
Work = Pressure * Area * displacement .....(3)

then recognise that
ΔVolume = Area * displacement

so
Work = Pressure * ΔVolume
 

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