MHB Maths in Temperature and ideal gas Thermometer

WMDhamnekar
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Hi,
I didn't understand the maths involved in the below article in regard to temperature and ideal gas thermometer. If any member knows it, may reply me.

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If triple point of water is fixed at 273.16 K, and experiments show that freezing point of air-saturated water is 273.15 K at 1 atm system pressure.(so, melting point of ice is also 273.15 K , then how triple point of water is $0.10^\circ C$ What is meant by real gas volume at thermal equilibrium with a system whose true temperature is $V_T$ be V. In this Math symbol$\big(\frac{\partial V}{\partial T}\big)_P$ what does subscript P indicate? My guess P means Partial.

I am stuck here. If get the answers to my questions satisfactorily, i shall proceed further.
 

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What, specifically, is it that you don't understand?

-Dan
 
Dhamnekar Winod said:
If triple point of water is fixed at 273.16 K, and experiments show that freezing point of air-saturated water is 273.15 K at 1 atm system pressure.(so, melting point of ice is also 273.15 K , then how triple point of water is $0.10^\circ C$

$0\,^\circ C$ is defined to be the freezing point of water at the standard 1 atm pressure.
It corresponds to $273.15\,K$.
Since the triple point of water is at $273.16\,K$, then that means that it corresponds to $0.01\,^\circ C$.

What is meant by real gas volume at thermal equilibrium with a system whose true temperature is $V_T$ be V. In this Math symbol$\big(\frac{\partial V}{\partial T}\big)_P$ what does subscript P indicate? My guess P means Partial.

I am stuck here. If get the answers to my questions satisfactorily, i shall proceed further.
The subscript $P$ in the expression $\big(\frac{\partial V}{\partial T}\big)_P$ stands for the pressure $P$.
It means that we take the derivative of $V$ with respect to $T$ while we keep the pressure $P$ constant.

We have $V=\frac{RT}{P}$ for an ideal gas.
When we take the derivative, we treat $P$ as a constant so that $\big(\frac{\partial V}{\partial T}\big)_P=\big(\frac{\partial}{\partial T}\frac{RT}{P}\big)_P=\frac{R}{P}$.
 
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