The mechanism that allows us to compute temperature values for pressure readings associated with a Helium filled glass bulb is based on how system properties are linked together. The purpose of using Helium gas is because Helium can remain in its gas state when surrounded by boiling liquid Nitrogen. The goal is to determine the temperature of a gas based on the pressure readings of that gas, so in order to determine a working equation, the ideal gas law will be modified to represent temperature.

T = P(V/nR) (1) There is a problem with using this equation due to the fact that we are not using an ideal gas. We are using Helium, so adjustments must be made to the ideal gas law in order for proper calculations to be computed. A route to
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This issue can be fixed by introducing the coefficient of linear thermal expansion of the glass bulb. In addition to the coefficient, we will multiply that value by three in order to satisfy the coefficient of volume expansion. A constant temperature will be assumed, so we will multiply the coefficient of volume expansion by t.

(pVo/RT)(1+(pv/prV)+3αt) = n. This equation still embraces how ideal gases interact within different temperatures, so the second virial coefficient is introduced. The second virial coefficient alters the equation by representing the imperfections associated with non-ideal gases. The second virial coefficient is also multiplied by (po/RTo) in order to relate the pressures of different environments to the pressure of the bulb submerged in an ice bath.

(pVo/RT)(1+(pv/prV)+3αt-(po/RTo)(B)) = n

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