mechanical equivalent to to heat

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Mechanical Engineering

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Jan 9, 2024

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Name Matthew Breeding MECHANICAL EQUIVALENT TO HEAT LAB Background Mechanical energy can be converted into heat, and heat can be converted into mechanical energy. This relationship is known as the mechanical equivalent to heat and it is an important concept fundamental to thermodynamics which applies ideas related to heat and work to create useful systems (i.e. power plants, engines, refrigerators …). The mechanical equivalent to heat phenomena was first tested by James Joule in 1843. In his experiment, he used the change in potential energy of a falling mass to stir water. As the water was stirred, the temperature of the water increased just like it was placed over a flame. This proved that the work done on a system (the falling mass) can be equated to an increase in water temperature (heat energy). Purposes • To determine the correlation between the height the mass falls and the change in temperature of the water. • To determine the correlation between the mass that falls and the change in temperature of the water. • To determine the specific heat of the water in the container. Materials • You will be running a simulation of the same kind of lab setup that James Joules used in the 19th century. This simulation can be found here . Part 1: Changing Height In this part of the lab, you are going to change the height of the falling mass and record the corresponding temperature change of the water. • Record the initial temperature of the water: 14.40 C • Select a value for the mass. To change the mass value, click on the mass. Record the value of the mass below. 320 kg • To change the height of the falling mass, click on the pulley. Start with the highest height and work your way to the lowest height. Be sure to measure height from the bottom of the mass. Click START to drop the mass and record the final temperature of the water. Click RESET to restart the simulation. Calculate the change in temperature of the water.

• Record all data in the table below: Height (meters) Final Temperature ( o C) Change in Temperature ( o C) 3.9 26.4 12.0 3.2 24.37 9.97 2.8 23.02 8.62 2.2 21.01 6.61 1.8 19.86 5.46 1.2 17.86 3.46 • To determine whether or not there is a correlation between the height the mass falls and the change in temperature , you are going to plot the data and perform a simple linear regression (i.e. draw a line through the data). Use the following resource to plot the data in this lab: Quick Graphing Program 5.0 . Plot height as the horizontal variable (the first data column) and change in temperature as the vertical variable (the second data column). Make sure to label each column. The program will automatically plot the points. After all points are plotted, select LINEAR from the GRAPH TYPE options. Include a screen capture of your completed graph here. • Record the correlation value calculated by the program. 0.99969 • In the space below, make a statement regarding the relationship between the height of the falling mass and the change in water temperature.

The higher the object the more the water spins, in other words, The higher the object the hotter the water gets. Part 2: Changing Mass In this part of the lab, you are going to change the value of the falling mass and record the corresponding temperature change of the water. • Record the initial temperature of the water: 14.4 • To change the value of the mass, just click on the mass. There are six different mass values. Start with the lowest mass value and work your way up. Drop each mass, record the final temperature of the water, then calculate the change in temperature of the water. • Record all data in the table below: Mass (kilograms) Final Temperature ( o C) Change in Temperature ( o C) 131 19.31 4.91 171 20.81 6.41 232 23.10 8.7 255 23.96 9.56 320 26.40 12 385 28.83 14.43 • To determine whether or not there is a correlation between the falling mass value and the change in temperature , you are going to plot the data and perform a simple linear regression (i.e. draw a line through the data). Use the following resource to plot the data in this lab: Quick Graphing Program 5.0 . Plot mass as the horizontal variable (the first data column) and change in temperature as the vertical variable (the second data column). Make sure to label each column. The program will automatically plot the points. After all points are plotted, select LINEAR from the GRAPH TYPE options.

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Include a screen capture of your completed graph here. • Record the correlation value calculated by the program. 1.00000 • In the space below, make a statement regarding the relationship between the falling mass value and the change in water temperature. The higher the Mass the faster the water will turn, in other words, the more mass the object has the hotter the water will be. Part 3: The Specific Heat of Water When James Joules performed this experiment in the 19th century, he was primarily trying to determine the amount of energy required to raise the temperature of a specific amount of water. Today, we refer to this quantity as the specific heat for a material. Using data from part 2 of this lab, you are going to experimentally determine the specific heat of water. • Transfer the mass and change in temperature values from your part 2 table to the table below. • Determine the work done by each mass in part 2 and record in the table below. The work done is equal to the potential energy that the mass contained prior to falling. W = PE = mgh The height that each mass falls in part 2 is 3.9 m, while g (the acceleration due to gravity) has a value of . • Recall that energy is conserved. As such, the work done on the system will equal the heat gained by the system.

Solving for the specific heat (c), we get ... Use this equation to calculate the specific heat of the water for each trail in part 2. Take note that if the beaker contains 296 ml of water, it will also be 296 g of water. Mass of water (m water ) : 239 g constant height = 3.9 m Record your values in the table below: Mass (kg) Work (Joules) Change in Temperature ( o C) Specific Heat of Water () 131 5006.82 4.91 4.27 171 6535.62 6.41 4.27 232 8867.04 8.7 4.26 255 9746.1 9.56 4.27 320 12230.4 12 4.26 385 14714.7 14.43 4.27 • Calculate the average specific heat of water value for this lab and record below: 4.265 • What does this number represent? this is the max