What is the Unknown Temp (T) in TL-TR Equation?

[Miike012]

The Question is in the paint document.

My question to this problem is at the bottom of thread 1
Equation:
T = T₃/P₃P. Where
T₃ is the temperature (K) of water at triple point
I am not 100% sure what P and P₃ stand for (can someone tell me)
I believe P is the net pressure (Pressure supplied by the bulb minus the pressure opposing the pressure supplied by the bulb)
and P₃ is the pressure at triple point.

Solution:
All Temp are in Kelvin (K)

Define:
T_L = Temp of left bulb
P_L = Pressure of left bulb
T_R = Temp of right bulb
P_R = Pressure of right bulb

First Step:

Let T_L = T₃ and T_R = Boiling Point of Water = (BP)

T_L - T_R = T₃ - (BP) =
T₃/P₃(P_L - P_R)

Because (T_L - T_R)<0 Then (P_L - P_R) = -120torr.

Solving for P₃:

P₃ =T₃(P_L - P_R)/(T₃ - (BP))

Second Step:
Let T_L = T₃ and T_R = Unknown Temp. (T)T_L - T_R = T₃ - T = T₃/P₃(P_L - P_R)

Solving for T:
T = T₃ - T₃/P₃(P_L - P_R)

QUESTION:
Because I don't know If T>T₃ or T<T₃ I do not know whether (P_L - P_R) = +90torr or -90torr.

How am I suppose to know?

 

[SteamKing]

The Paint document didn't make it thru the posting process. Please repost the attachment.

 

[Miike012]

I figure it out:

Let T_L = Temp left bulb
P_L = Pressure Left bulb
and
T_R = Temp right bulb
P_R = Pressure Right bulb

I will keep T_R constant at triple point and vary T_L:

First Phase: The pressure difference was 120torr when one bulb was at triple point and the other was at boiling point.

If P_L - P_R = 120then T_L>T_R


Second Phase: The pressure difference was 90torr when one bbulb was at triple point and the other was at an unknown temperature (T)

If P_L - P_R = 90 then T>T_R