Pressure, Volume, Temperature Relationships

Lab Day 3: March 2, 2015 Relationships between Pressure, Volume, and Temperature

Pressure:
Can Experiment:

Lipton Iced Tea Can predictions

In this experiment, we predicted that the iced tea can will rapidly implode because the gas wants to escape the can due to the pressure built up inside from the heat.

Heating the bottom of Lipton iced tea can with a torch
 (steam is present)

The iced tea can did in fact implode as predicted where we see that the can had air inside from heating and it imploded instantly. 

Only hot air experiment

After putting it in water

Predictions of just hot air in the can

On the other hand, with only hot air, the can sucked in water as seen in the picture.

Analysis of units in pressure

Project 1:Pressure Vs. Volume Relationship

In this experiment an syringe was setup where we compressed air in small increments to change the volume and pressure.

Quadratic fit graph logger pro data

The quadratic fit is seen a bit off from the curve therefore, the second linear fit is a better fit for the relationship.

Fit parameters on logger pro results

The shape of this fit in the experiment we performed showed that it has a relationship that is inversely proportional. Therefore we analyzed the graph and had a linear and quadratic fit where we chose the linear fit to be a better fit for pressure vs volume relationship. The graph is a curved shape where the volume decreases as the pressure increases. In the beginning, there is a sharp reduction in the volume as the pressure increases. The decrease in volume then becomes more gradual and the volume appears to level off as the pressure increases further. It is some sort of hyperbolic curve where it is obtained through the inverse relationship between the two variables where y=A/x.

Simple Representation of inverse relationship

calculations of units of pressure

The slope from the fit was used to find the units of pressure above.

Project 2: Pressure Vs. Temperature Relationship

    

Charles law relationship of Pressure and Volume predictions

Apparatus of Pressure vs temp.

The apparatus used was to measure pressure vs. temperature where the flask was the test volume of gas and by immersing the flask in a container of heated water, we added ice chips to measure the relationship. 

Logger pro graphical representation of pressure vs temp relationship

Simple representation of P vs T (Charles Law concept)

In fact the graph shows results of a straight line where it is a proportional relationship in which the pressure remains constant even if the volume of air in the system changes because the greater pressure on the inside of the container walls will push the gas outward which increases the volume. As a result, the gas molecules will have more space to go, therefore lowering the number of collisions and decreasing the pressure to its constant value.

Project 3: Volume Vs. Temperature Relationship

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In this experiment, the beaker is filled with water where we added ice to the reduce the volume of the trapped air, where we pulled the plunger out at the 9 cc mark. 

Volume vs Temperature Relationship 

The results show that the volume is directly proportional to the temperature of gas in which doubling the temperature will also double its volume and the slope is constant. Charles law is also represented in this case.
Boltzmann/ univeral gas constant

Relationship of Boltzmann constant and universal gas constant (Avogradro's number relationship)

Diving Bell Problem:

Diving Bells Calculations Part A: Pressure total

Diving Bells Calculations Part B: Height

This problem was an great example of diving bells and the idea of pV=nRT where we have changes in height and a relationship between pressure, volume and temperature in one problem that applies the gas relationships we experimented and analyzed.

Marshmallow Experiment:

Marshmallow predictions (Pressure and Volume)

Marshmallow apparatus where pressure can be sucked out and in for the vacuum.

Video on marshmallow experiment

In this part when the pressure decreases, the volume increases where our marshmallow expanded as we sucked out the pressure from inside. (unfortunately some marshmallow pictures were deleted :(( ) but it got bigger from the observations. On the other hand when the pressure increased, the volume decreased causing the marshmallow to get smaller. When it went back to the initial state, the marshmallow became shriveled because the air escaped.

Balloon: calculations of maximum mass of helium in the balloon

We were able to identify three different relationships between pressure, volume, and temperature in different experiments. The first experiment observed that the pressure and volume had an inverse proportional relationship that shows that the volume increases as the pressure decreases. Another experiment analyzed the proportional fit of a straight line where pressure remains constant even when the volume changes in correlation to the temperature. The last experiment showed that volume is also directly proportional to temperature where the slope is constant. These ideas based on Boyle's and Charles law helped us derive the equation of the ideal gas law where the three experiments were all in effect using Boltzmann's constant and the universal gas constant. The results seen in the can and marshmallow experiment, showed that pressure, volume, and temperature can be used to determine the interactions of gases.

Thermal Expansion and Latent Heats

Lab Day 2: February 26, 2015 Thermal Expansion and Latent Heats

Expansion of ball and ring

In this experiment, we predicted that the brass ring will expand and the hole in the middle will get bigger after being heated. As we heated the ring with a torch, the observations of the hole did in fact expand and get bigger which allowed the ball inside to also expand through which is consistent with our predictions. Due to linear thermal expansion, the atoms will move apart and the hole size will increase as the hole will expand in the same ratio as the metal. Every portion of the ring will expand which therefore leaves a bigger hole because it gets larger with the other parts of the ring expanding outward. 

Torch and ball in a ring: the ball in the middle expanded with the ring after heat

Thermal Linear Expansion

Thermal expansion:

When the temperature changes as a bar is heated, the initial length and the type of material are variables that will affect the change in length in linear thermal expansion. In volume expansion it is the same idea but using volume of the object with the material coefficient of volume expansion.

Bimetallic Strips heated

The bimetallic strip bent toward the invar side with the brass side on the right.

The bimetallic strip that consists of brass and invar was heated on the brass side which showed that brass expands faster where the strip will bend to the right because it will push toward the invar side which expands slower. 

However, when the bimetallic strip was placed in ice, the strip bent to the left toward the brass side because the brass shrinked which caused the strip to pull and bend less to the right and more to the left. 

Bimetallic strip in ice observations (bent to the left: the right side is invar and the left side is brass)

Metal rod clamped to a rotary motion sensor

Linear Expansion Demo
 (a meter long metal rod connected to a rotary sensor on one side as steam is heating up the rod)

Close up view of steam blowing through the rod to add heat.

Graph of linear thermal expansion of temperature vs time and angle vs time

linear expansion demo: Setup for angular displacement and linear distance/Symbolic calculations for coefficient of thermal expansion

Numerical calculations for coefficient of thermal expansion 

Uncertainty Propagation: variables L, r, theta, and T

Uncertainty Propagation of linear coefficient of thermal expansion

There was systematic error found in poor calibration of the setup where the temperature could be off by an uncertainty of +/-0.05. The radius was measured by unknown in which could have assisted to a big percentage of the error in our results. The length measured by a meter stick was measured to have an uncertainty (with a precision half of the smallest increment) of 0.005 m. Another source of error found could be the lag time of the sensors or instrument used that caused the thermal equilibrium to be off by a little. 

Based on the value calculated for coefficient of thermal expansion, the material is made up of brass which is the same as the listed value found in the tables for brass. The coefficient is pretty big which means that the rod will expand quickly.

Heating water:

Predicted shape of heating "curve"

Before picture of graph initial mixing

Graph results of heat energy transfer at constant rate to water mixture

Latent heat of fusion of water Calculations

The calculated value of of latent heat and the graph shows that breaking bonds in ice is much easier than steam. We can therefore identify that the heat of fusion and vaporization as Q=mL.

The final temperature and mass of ice.

This answer came out to be incorrect because it is below 0 degree celsius if we assumed that all the water melted. However, ice does not melt completely based on these calculations where the final temperature is 0 degrees C because the final state is a mixture of ice and water.

Another group calculation of mass value

Water on the rocks problem:

In this system water is added to a system filled with ice. This is a conservation of energy problem.

In this situation, the heat gained is equal to the heat loss based on the conservation of energy and the mass of water is found from identifying the heat gain in the melting of ice and the heat loss from the change from liquid ice to final temperature along with the heat loss in water. If we added less water, there would still be ice remaining in the system at a lower temperature.

Pressure:

We measured the gas pressure with a manometer where we added water to the bottom of the tube and blew on it. Initially, the pressures on each side are the same at the same water levels where P1=P2. However when pressure increases on one side, P1>P2. Based on the change in height and the pressure of water the pressure can be derived to be P=hpg using density, volume, and pressure.

Pressure symbolic calculations from manometer

We focused on the idea of thermal expansion in terms of linear, volume, and area. The change in temperature (heating or cooling of a solid) is seen to cause objects depending on the material to expand as seen in the bending of the bimetallic strip and the heating of the brass ball in the ring. The outward expansion of the hole in the ring indicates that expansion occurs at the same ratio with the material. The linear expansion demo was consistent with thermal expansion where we further identified the rod to be a brass material which expands quickly.This relates to the importance of thermal expansion in the building of structures where there has to be enough space to prevent stress from temperature differences. We also observed adding of heat to water and the changes in phases which is applied in systems using the concept of conservation of energy. The idea of melting or evaporation is seen in phase changes that occur in ice and water using the latent heats of fusion or evaporization that is significant in determining the heat gained equal to the heat lost idea in changing systems. Pressure of gases was analyzed using a manometer where the ideal gas law pv=nRT is observed using pressure, volume, and absolute temperature. The pressure of the column of liquid was derived using the height, volume and pressure along with its area. The ideal gas law is seen to work the best when gas pressures are low and temperatures are high where the model has some limits, but at ideal states it works well in describing its relationships.