4.02 Absolute Zero
Using the graph or the equation, answer the following question: A fixed mass of gas at initial pressure of 5.0 Pascals and absolute temperature of 200. K will be at what absolute temperature when the pressure is 8.0 Pascals? P1 = 5.0 Pascals T1 = 200. K P2 = 8.0 Pascals T2 = ?
P1/T1 = P2/T2 T2 = (P2T1)/P1 T2 = [(8.0 Pascals)( 200. K)]/5.0 Pascals T2 = 320 K If you look at the graph you will see that the absolute temperature reading for 8.0 Pascals of pressure is approximately 320 K.
Analyzing the graph (^):
A fixed mass of gas in an enclosed rigid container with an initial pressure of 5.0 Pascals and absolute temperature of 200. K is heated such that the gas reaches an absolute temperature of 400. K. What will the pressure be when the gas reaches the absolute temperature of 400. K (Notice the absolute temperature doubled)? The equation for a straight line: y = m x P = k T P1 = k T1 P2 = k T2 Solving equation for constant of proportionality k: k = P/T k = P1/T1 k = P2/T2 Setting the constant equal to each other gives you the equation for Gay-Lussac's Law: k = k Therefore: P1/T1= P2/T2
Gay-Lussac's Law
states the following: "When the volume of the enclosed gas and the number of molecules of the enclosed gas remain the same, the absolute temperature is directly related to the pressure exerted by the enclosed gas." As the absolute temperature increased, the average kinetic energy of the molecules increases. The molecules collide with the container walls with a greater force and more frequently. This relationship is: P α T P is the pressure α denotes a relationship T is the absolute temperature of the gas (Kelvin)
The Gas Law of Gay-Lussac (Joseph Gay-Lussac: 1778-1850):
Although gases do not have a definite shape or a definite volume, except for that defined by their containers, a relationship between temperature and volume can be developed for enclosed gases. The product of the pressure and the volume of an ideal gas is directly proportional to the product of the number of molecules in the gas and its absolute temperature. This proportionality expressed mathematically as: PV α nT P is the pressure V is the volume α denotes a relationship n is the number of molecules T is the absolute temperature (Kelvin)
Definition of Absolute Zero:
In his book Conceptual Physics, Paul Hewitt defines absolute zero as "the temperature at which a substance has no kinetic energy per particle (thermal) to give up." This temperature corresponds to zero Kelvin.
Introduction:
In principle, there is no upper limit to temperature. As thermal motion increases, a solid object first melts and then vaporizes. As the temperature is further increased, molecules break up into atoms, and atoms lose some or all of their electrons, forming a plasma. Plasmas exist in stars where the temperature is many millions of degrees Celsius. However, there is a definite lower limit to temperature. Experiments in the 19th century showed that there is a limit to coldness. At this lowest temperature, no more energy can be extracted from a substance. What is the lowest possible temperature? The name absolute zero has been given to the lowest possible theoretical temperature.
Temperature and Absolute Zero:
It was also found that the pressure of any gas in a chamber of fixed volume would change by 1/273 for each one degree Celsius change. So gas in a container of fixed volume cooled to -273 Celsius would have no pressure whatsoever. In reality, every gas becomes a liquid before it gets this cold.
Pressure and Absolute Zero:
The value of absolute zero was found in the 1800s by experimenters who discovered that all gases contract by the same proportion when temperature is decreased. It was found that any gas at zero degrees Celsius, regardless of its initial pressure or volume, changes by 1/273 of its initial volume for each one degree Celsius change in temperature, when pressure is held constant. For example, when the temperature is reduced to -100 degrees Celsius, the volume of the gas is reduced by 100/273. More striking, if a gas at zero degrees Celsius were cooled to -273 degrees Celsius, its volume would be reduced by 273/273 and become zero. Clearly, we cannot have a substance with zero volume.
Kinetic Energy and Absolute Zero:
These decreases in volume and pressure by increments of 1/273 suggested the idea of the lowest possible temperature (-273 Celsius). This temperature is called absolute zero. Keep in mind, however, that at absolute zero atoms have a small amount of kinetic energy called zero-point energy.