# Ideal Gas Temperature scale

## Homework Statement

the gas scale temperature is defined as:

T=273.16 lim Ptp->0 (P/Ptp)

The bulb of a constant volume gas thermometer is immersed in an ice-water-vapour mixture and the recorded pressure is 0.500 atm. It is then immersed in a boilng liquid and the pressure is 0.720 atm. Some gas is removed from the bulb and the experiment repeated, registering 0.250 and 0.350 atm respectively. Estimate, as accurately as possible, the boiling temperature of the liquid. 

## The Attempt at a Solution

So here Ptp is recorded as 0.5 and 0.25, with corresponding P's of 0.72 and 0.35 right? Would it be better to take the average value calculated or use only the lower value of Ptp as it closer to 0? I'm a bit confused.

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The boiling temperature of the liquid is approximately 382.424 K.

You have to understand what the Ideal-gas Temperature Scale actually means.

$$T = T_{TP} \lim_{P_{TP}\to\ 0} (\frac{P}{P_{TP}})$$

The above equation, states that the temperature of the substance which you are measuring (in this case the boiling liquid) is given by a function of the Triple Point of water (273.16 K) times the ratio of the pressure of this boiling liquid by the pressure of the Triple Point of water. The limit is used to show that as the Triple Point pressure goes to zero, the more accurate will be the temperature to be measured.

Therefore, you will work with the lowest measures provided. As the more accurate temperature will be given as $$P_{TP} \rightarrow 0$$.