Temperature change of water at triple point in a constant-volume gas thermometer

In summary, the triple point of water is the temperature and pressure at which water can exist in all three states simultaneously. A constant-volume gas thermometer measures temperature change at this point by using the principle that the pressure of a gas is directly proportional to its temperature. The triple point of water is used as a reference point for temperature measurement due to its well-defined and reproducible nature. Measuring temperature change at the triple point allows for high precision and accuracy, and is also used as a calibration point for other temperature measurement devices. However, there are limitations to using a constant-volume gas thermometer, such as its inability to measure temperatures below freezing and potential inaccuracies due to impurities and sensitivity of the instrument.
  • #1
aeluik
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Homework Statement


P(at triple point in torr of water) 100 200 300 400
P(in torr for gas w/ respect to Pressure above) 127.9 256.5 385.8 516.0

The previous table gives the observed values of the pressure of a gas in a constant-volume gas thermometer at an unknown temperature T and at the triple point of water as the mass of the gas used is reduced. Determine T in kelvins by considering the limit of the pressure of the triple point as it approaches zero of (P(gas)/P(triple point of water).


Homework Equations


P=aT+b
T(K)= 273.16lim(Ptp->0)(P/Ptp)


The Attempt at a Solution


I don't even know where to go with this. I have no clue where to start. I've tried a bunch of random things, but it all goes nowhere.
 
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Thank you for your question. I can offer some guidance on how to approach this problem.

Firstly, let's define some variables. Let Ptp represent the pressure at the triple point of water and let Pg represent the pressure of the gas at an unknown temperature T. We also know that the pressure of the gas can be represented by the equation P=aT+b, where a and b are constants.

We are given a table with the observed values of Ptp and Pg at different temperatures. We can use this table to create a graph with Ptp on the x-axis and Pg on the y-axis. This will give us a straight line with a slope of a and an intercept of b.

Next, we need to consider the limit of Ptp as it approaches zero. This means we need to look at the behavior of the graph as Ptp gets smaller and smaller. We can see that as Ptp gets closer to zero, the value of Pg also gets closer to zero. This means that the slope of the graph, which represents a, also approaches zero.

Finally, we can use the equation T(K)= 273.16lim(Ptp->0)(P/Ptp) to determine the unknown temperature T. We know that as Ptp approaches zero, the value of P/Ptp will approach a constant. This means that the limit of P/Ptp is equal to this constant, which we can call c. Therefore, we can rewrite the equation as T(K)= 273.16c.

To find the value of c, we can use the data from the table. We can take any two points and calculate the value of P/Ptp. For example, if we take the first two points (Ptp=100 and Pg=127.9), we get c=1.279. We can do this for all the points and take the average value of c to get a more accurate result.

Once we have the value of c, we can plug it into the equation T(K)= 273.16c to find the temperature T in kelvins.

I hope this helps guide you in solving this problem. Good luck with your research!
Scientist
 

1. What is the triple point of water?

The triple point of water is the temperature and pressure at which water can exist in all three states (solid, liquid, and gas) simultaneously.

2. How does a constant-volume gas thermometer measure temperature change at the triple point of water?

A constant-volume gas thermometer uses the principle that the pressure of a gas at a constant volume is directly proportional to its temperature. By measuring the pressure of the gas at the triple point of water, the thermometer can determine the temperature of the water.

3. Why is the triple point of water used as a reference point for temperature measurement?

The triple point of water is used as a reference point because it is a well-defined and easily reproducible state that is not affected by external factors such as pressure. This makes it a reliable standard for temperature measurement.

4. What is the significance of measuring temperature change at the triple point of water?

Measuring temperature change at the triple point of water allows for highly accurate and precise temperature measurements, as it is a stable and well-defined point on the temperature scale. It is also used as a calibration point for other temperature measurement devices.

5. Are there any limitations to using a constant-volume gas thermometer to measure temperature change at the triple point of water?

Yes, there are some limitations. The main limitation is that the thermometer can only measure temperatures above the freezing point of water (0 degrees Celsius). Additionally, the accuracy of the measurement can be affected by impurities in the water or gas used, and the sensitivity of the instrument.

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