How Is Thermodynamic Temperature Calculated for a Gas at the Triple Point?

[stockill92]

Hello, new to these forums

I'm trying to complete a basic thermodynamics problem, calculating the thermodynamic temperature of a gas immersed in water at triple point.

The problem begins with a table of pressures at varying temperatures of a gas under pressure P, and pressure P(tp) - triple point pressure.

Now, I know the following equation;

T=LIM_PTP→0P/P_TP * 273.16​

So I have calculated the average value of P/P_TP as 1.53555

But I also have access to a solution to this problem, and in the solution an extra step is also taken:

I don't understand the source of the 2.5 * avg change between P and P(tp). Where has this come from? Why is it necessary?

Thanks

 

[Philip Wood]

I don't understand either, but rather than trying to do so, I've used a more straightforward method. I evaluated P/P_tp to 5 decimal places for each of the five pairs of readings. It was then clear that the ratio increased by almost the same increment for each 250 mmHg decrement in P_tp. Hence naïve extrapolation of P/P_tp to zero pressure is very straightforward.