Volume Expansivity of Ideal Gas

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SUMMARY

The volume expansivity, β, for one mole of an ideal gas at constant pressure and room temperature is calculated using the formula β=1/V(dV/dT). By applying the ideal gas law (PV=RT) and recognizing that dV/dT equals R/P when pressure is constant, the final expression for volume expansivity simplifies to β=1/T. This conclusion provides a clear relationship between volume expansivity and temperature for ideal gases.

PREREQUISITES
  • Understanding of the ideal gas law (PV=RT)
  • Familiarity with calculus, specifically differentiation
  • Knowledge of thermodynamic concepts such as volume expansivity
  • Basic principles of gas behavior under constant pressure
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  • Learn about the implications of volume expansivity in thermodynamics
  • Explore the relationship between temperature and pressure in gas laws
  • Investigate real gas behavior and deviations from ideal gas assumptions
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Homework Statement


Calculate the volume expansivity, β, for one mole of ideal gas at constant pressure and at room temperature.


Homework Equations



β=1/V(dV/dT)

The Attempt at a Solution



Bit stumped on this one, I'm guessing they want it in terms of P as P is not specified.
I used equation of state with n=1 giving PV=RT

> V=RT/P

> β=P/RT(dV/dT)

As the temperature and pressure are constant would dV/dt be zero?
Its from here I am stuck :confused: , any help welcome

Thanks
 
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If V=RT/P, then (dV/dt) = R/P for P = const. Therefore
$$
\beta = \frac{1}{V} \left( \frac{d V}{d T} \right) = \frac{P}{RT} \frac{R}{P} = \frac{1}{T}
$$
 

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