Question: Determining absolute zero with a piston

[PrinceOfDeaf]

I am working on a lab report related to Ideal Gases at the moment, and I can't quite grasp how you would go about finding the temperature for absolute zero. Here's a brief synopsis of our experiment: We inserted a piston into a cylinder of water to keep the piston at a steady temperature of 23 degrees Celsius. Then, we placed known masses on top of the piston and measured the height change, thereby allowing us to determine the pressure that the gas exerts (1kg, 2kg, ..., 5kg). We repeated this experiment but now with ice in the water, and this changed the system to be at a steady 3 degrees Celsius. We graphed height vs 1/pressure for both cases and computed regression lines if that has any significance to the question at hand.

How would you go about extrapolating absolute zero from this experiment?

 

[Mapes]

Hi PrinceofDeaf, welcome to PF. What is the ideal gas law? What quantity (hint: what product) would be zero at $T=0\,\mathrm{K}$?

 

[tomcue]

I would approach this question by first understanding the concept of absolute zero and how it relates to the behavior of ideal gases. Absolute zero is the theoretical temperature at which the particles of a gas have zero kinetic energy, meaning they are completely motionless. This is the lowest possible temperature that can be reached, and all other temperatures are measured relative to it.

In order to determine absolute zero using a piston, we need to use the ideal gas law, which states that the pressure, volume, and temperature of an ideal gas are all directly proportional. In your experiment, you have measured the pressure and volume of the gas at two different temperatures (23 degrees Celsius and 3 degrees Celsius). By plotting the data and computing regression lines, you have essentially created a graph that shows the relationship between pressure and volume at different temperatures.

To extrapolate to absolute zero, we need to find the point on the graph where the volume would be zero, which would correspond to absolute zero temperature. This can be done by extending the regression line until it intersects with the x-axis, which represents a volume of zero. The temperature at this point would be absolute zero.

However, it is important to note that this method is an approximation and may not be completely accurate due to experimental errors and the fact that real gases deviate from ideal gas behavior at very low temperatures. Therefore, it is important to recognize the limitations of this method and to compare the results with other methods of determining absolute zero.

In conclusion, determining absolute zero with a piston involves using the ideal gas law and extrapolating data from a graph to find the point where volume would be zero. This method can provide a rough estimate of absolute zero, but it is important to consider potential sources of error and to validate the results with other methods.