Is all heat added to a gas converted into pressure change?

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    Gas Pressure Variation
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Discussion Overview

The discussion revolves around the relationship between heat added to a gas and its resulting pressure change, particularly in the context of thermodynamic processes such as isothermal expansion and constant volume conditions. Participants explore the implications of specific heat, work done by gases, and the conditions under which pressure may change.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions whether it is possible for heat added to a gas to result solely in a change in pressure without affecting internal energy, suggesting a hypothetical scenario.
  • Another participant asserts that the work done by a gas is not simply PV, emphasizing the need to integrate over the specific process to determine work accurately.
  • A participant raises the issue of whether changes in pressure need to be treated as independent variables in calculations related to work or specific heat.
  • Concerns are expressed regarding isothermal expansion, with one participant questioning if maintaining constant temperature guarantees that pressure remains unchanged after expansion.
  • Another participant reiterates that work done by a gas requires consideration of volume changes and challenges the notion of work being defined as PV.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between heat, pressure, and work done by gases. There is no consensus on whether heat can be entirely converted to pressure change or the implications of isothermal processes on pressure.

Contextual Notes

Participants highlight the complexity of thermodynamic processes, noting that assumptions about constant volume or pressure may not hold in all scenarios. The discussion reflects varying interpretations of work and heat transfer in gases.

Who May Find This Useful

This discussion may be of interest to those studying thermodynamics, particularly in understanding the nuances of heat transfer, work done by gases, and the implications of different thermodynamic processes.

collectedsoul
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Work done by a gas = PV

But when we derive specific heat of the gas at constant volume, even though the pressure changes we take work W=0. Or in the case where both pressure and volume are changing and we want to find work done we take the integral of d(PV) where we replace P with nkT/V. Also when we want to find change in heat content [itex]\Delta[/itex]Q, we equate it to internal energy [itex]\Delta[/itex]E + [itex]\Delta[/itex](PV). If volume is kept constant we eliminate the term [itex]\Delta[/itex](PV). So does that mean that its not possible to add heat to a gas and have it all go to the change in pressure of the gas, i.e., a hypothetical situation where internal energy does not change but pressure does change?

My second question is - is there ever a scenario where dP needs to be taken as an independent variable to find work done or to find some other characteristic of the gas (like Cv)?

Another thing I'm confused about is the case of an isothermal expansion. When the gas expands by a volume dV we have to put in heat to keep it at the same temperature as before. If we do that, is it possible that in the final equilibrium state the pressure might be different from what it was initially? Or is constant pressure guaranteed by the condition of maintaining the same temperature post expansion?
 
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collectedsoul said:
Work done by a gas = PV
The work done by a gas is not PV.
For the special case of a process at constant pressure you can use [tex]W=p\Delta V[/tex]
In general, you need to integrate [tex]dW=p dV[/tex] over the specific process to find the work.
 
nasu said:
The work done by a gas is not PV.

Is anything that we are interested in require an integral over small changes in pressure?
 
collectedsoul said:
Is anything that we are interested in require an integral over small changes in pressure?

Work involves a force moving through a distance. If you don't change the volume then there is no distance moved - so no work. Just in the same way that no work is done as you add more weights onto the top of a table - if it doesn't flex at all.
 

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