Thermal Equilibrium and Latent Heat

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Temple University *

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1021

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Chemistry

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Jan 9, 2024

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Title: Thermal Equilibrium and Latent Heat Group 33: Van Tran, Elyse Gallagher, Shrenik Patel Experiment Date: November 28th, 2023 Goals: The goal of today’s lab is to practice calculating changes in heat and temperature for water, practice using conservation of energy to calculate unknown values and become familiar with the concept of latent heat Procedure: Part I: Start with a sample of 100mL of hot water and add cold water 100mL at a time Measure how the temperature is change as we mix in the cold water Make a table in Excel for recording the values Fill a large container with at least 400 mL of cold tap water and transfer 100 mL into each of the three graduated cylinders Then pour 100 mL of the cold tap water into the metal container and place it on the hot plate and heat until it is about 75ºC When hot water reaches about 75ºC, put on thermal safety gloves and pour the hot water into the Styrofoam calorimeter cup taking care to not spill any Measure and record the temperature of the first cold sample and the hot sample and then immediately mix the cold sample into the hot one Stir them together for a couple of seconds and then record the final temperature Complete the table and then graph the data collected Part II: Fill the double Styrofoam cup to the brim with wet ice (wet ice is ice that is at 0 °C) Place the cup in the top of the graduated cylinder so water from the melted ice will drip into the graduated cylinder Place a temperature probe at the bottom of the graduated cylinder to measure the final temperature Measure off 200 mL of hot water at about 80 °C. Measure and record the initial temperature of the hot water Pour the hot water very slowly onto the ice in the Styrofoam cup Use the temperature probe in the bottom of the graduated cylinder to stir the water once or twice then record the final temperature of the water Calculate the amount of heat lost by the hot water Precautions and Sources of Error : The exact amount of water in each cylinder and the
temperature for hot water could be slightly off since we have to use our best judgment when measuring. Data: Sample of calculations Q=mcΔT Q= (100g) (1 cal)(20 ) Q = 2000 cal Warm Water Mass (g) Initial Temp ( ) Final Temp ( ) Δ T ( ) Heat lost by warm water (cal) 100 75 55 20 2000 200 55 49.5 5.5 1100 300 49.5 43 6.5 1950 Cold Water Mass (g) Initial Temp ( ) Final Temp ( ) Δ T ( ) Heat lost by warm water (cal) 100 23.7 55 31.3 3130 200 23.7 49.5 25.8 5160 300 23.7 43 19.3 5790 Here is a link to the data table (will insert once completed) https://docs.google.com/spreadsheets/d/1Skh5rIfEGo_zjYrv1BQ3tuA2CIjDCxz3ZDdOe_3Ygu w/edit?usp=sharing Tf - 17.9 ΔT HW = Tf - 80 ΔT CW = Tf - Ti L = [(-M HW )(C W )(ΔT HW ) - (M CW )(C W )(ΔT W )] / M ICE L = [(-0.2kg)(4181 J/kg )(17.9 - 80) - (120 mL * 10^-6 * 1000)(4181 J/g )(17.9)] / (120 mL * 10^-6 * 1000)
L = 357893.6 or 3.57893 * 10 ^5 J/kg Theoretical: 3.33 * 10 ^5 J/kg Percent Error [ 3.57893 * 10 ^5 - 3.33 * 10 ^5 ] / 3.33 * 10 ^5 (100) = 7.5% Questions: Question 1. What does the resulting slope imply about the relation between the heat lost by the warm water and the heat gained by the cold water? The resulting slope shows that there is a direct relationship between the heat lost and heat gained because in theory the values should remain the same because of the first law of thermodynamics. Question 2. Assuming that the system is isolated from the surroundings, derive an expression for the latent heat of fusion of water in terms of measurable quantities. To do this start with the fact that all the heat that leaves the hot water will go into melting the ice and further heating the resulting water: leaving hot water * = melting ice + into cold water * * * * * * * * * * * * * * * (M HW )(C W )(ΔT HW ) + M ICE L + (M CW )(C W )(ΔT W ) = 0 L = [(-M HW )(C W )(ΔT HW ) - (M CW )(C W )(ΔT W )] / M ICE Question 3. We can’t directly measure the ice volume so how do you find the volume of the ice that melted? We can calculate this by subtracting the hot water mass from the total mass in the cylinder. Discussion: In the first part of the lab we observed changes in heat and temperature for water. We observed that the water temperature decreased every time cold water was poured into the mixture. The opposite occurred when we observed the cold water, we saw the cold water gets warmer. We used Q = MCΔT to calculate the heat lost or gained during the experiment. In the second part of the lab the procedure involved using a double Styrofoam cup filled with wet ice. The cup had a hole at the bottom, allowing melted ice to drain into a graduated cylinder placed beneath it. A temperature probe was positioned at the bottom of the graduated cylinder to measure the final temperature. We did this by filling a double styrofoam cup with ice and then measuring approximately 200 mL of water to 80 . We then poured the water slowly into the styrofoam cup, stirring the water in the graduated temperature, in which we measured a final temperature of 17.9 . We then calculated the volume of ice by subtracting the total volume of
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the cylinder by 200 mL in which we calculated a total volume of 120 cm 3 of ice. We then used the equation from question 2 to determine the latent heat of fusion of water. Our value came to be 3.57893 * 10 ^5 J/kg.