Maths in Temperature and ideal gas Thermometer

In summary: This means that the real gas volume is equal to the ideal gas volume multiplied by the pressure.In this case, the pressure is $P$ and the real gas volume is $R\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,
  • #1
WMDhamnekar
MHB
378
28
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.

1602763019755.png


1602763122516.png

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.
 

Attachments

  • 1602763093491.png
    1602763093491.png
    34.8 KB · Views: 75
Mathematics news on Phys.org
  • #2
What, specifically, is it that you don't understand?

-Dan
 
  • #3
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 $\big(\frac{\partial V}{\partial T}\big)_P=\big(\frac{\partial}{\partial T}\frac{RT}{P}\big)_P=\frac{R}{P}$.
 
Last edited:

FAQ: Maths in Temperature and ideal gas Thermometer

1. How is temperature measured using an ideal gas thermometer?

An ideal gas thermometer measures temperature by using the relationship between pressure and volume of a gas at a constant temperature. As the temperature increases, the volume of the gas also increases, resulting in a higher pressure. By measuring the change in pressure, the temperature can be determined using the ideal gas law.

2. What is the ideal gas law and how is it used in temperature measurement?

The ideal gas law, also known as the universal gas law, is a mathematical equation that describes the behavior of ideal gases. It states that the pressure, volume, and temperature of an ideal gas are related by the equation PV = nRT, where P is pressure, V is volume, n is the number of moles of gas, R is the gas constant, and T is the temperature in Kelvin. This equation is used in temperature measurement by relating the change in pressure to the change in temperature.

3. How does the ideal gas thermometer differ from other types of thermometers?

The ideal gas thermometer differs from other types of thermometers in that it does not use a physical substance, such as a liquid or metal, to measure temperature. Instead, it relies on the behavior of an ideal gas and the ideal gas law to determine temperature. This makes it more accurate and precise, as it is not affected by the properties of the substance used in other thermometers.

4. What are the limitations of using an ideal gas thermometer to measure temperature?

While the ideal gas thermometer is highly accurate and precise, it does have some limitations. One limitation is that it can only measure temperatures within a certain range, as the gas may become too compressed or expanded at extreme temperatures. Additionally, the ideal gas law assumes that the gas is ideal, meaning it has no intermolecular forces or volume. In reality, no gas is truly ideal, so there may be slight discrepancies in the measurements.

5. How is the ideal gas thermometer used in scientific research and experiments?

The ideal gas thermometer is commonly used in scientific research and experiments because of its high accuracy and precision. It is often used in studies involving gases, such as in chemistry or physics experiments. It is also used in industries that require precise temperature measurements, such as in manufacturing processes. Additionally, the ideal gas law can be applied to various other systems, making it a useful tool in many different fields of science.

Back
Top