PHYS4B PTChiou: First Law of Thermodynamics 3/3/2014

Today we began Gas Laws with the lab Volume vs. Temperature. With glass syringes from the 70's to minimize friction, we replicated the lab Prof Mason did in the previous lecture.:

Glass syringe rises as the air heats up/pressure/volume increases and glass syringe drops as air cools/pressure/volume decreases.

Recorded Lab results

This purpose of this lab is to record and plot the data of Volume vs. Temperature using graphing software. Once obtaining the data, we derived how V and T are related proportional mathematically.

We then summarized these relationships based on how pressure depends on temperature at constant volume, and how volume depends on temperature at constant pressure, and how pressure and volume are related at a constant temperature.

Describing the relationship between volume and temperature in terms of V, T, and C₁ when the pressure is held constant (C₁is a constant)

Describing an equation of Charles’ law II we discovered in in terms of P, T, (and another constant, C₂)

Multiply the two relationships together and summarize the results in terms of P, V, T, (and a third constant denoted C₃)

Finally, by deriving the third we magically (or Algebraically) came up with

The Ideal Gas Law describes all three relationships mathematically in an idealized fashion. It is given by:

PV = nRT

where P is pressure, V is volume, n is the number of moles of molecules, T is the absolute temperature, and R is the gas constant (8.314 joules per degree Kelvin or 1.985 calories per degree Celsius).

In words, the Ideal Gas Law is the relationships between measurable properties of an ideal gas. The law suggests under constant pressure and temperature conditions, the volume of a gas depends solely on the number of moles of its molecules, not on the type of gas.

The constant 'R' is there to allow for a direct relationship among the other values, (P, V, n, T). It is there to account for all the different units of measure: atmosphere, liter, mole, and kelvin. The formula PV=nRT, proportionality will indicate that when a value on the left of the equal sign increases, either some value on the right will also increase (except for 'R') or the other value on the left will decrease (inversely proportional). The experimentally derived constant R allows us to calculate the amount of the change of the other components.

For the rest of the day, we spent our time theoretically deriving, and working on word problems:

The pressure of the air inside the diving bell as it descends by manipulating our golden "Gas Law" equations.

The number of moles of molecules "n" inside the bell remains constant because no air escapes.

When the surrounding pressure decreases, the balloon expands due to its internal higher pressure. As the pressure decreases, it equalizes back to equilibrium.