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.