Lab 2
The Ideal Gas Law and Heat Transfer
OBJECTIVES
1. Experimentally verify the Ideal Gas Law for air.
2. Predict and measure Absolute Zero temperature the Universal Gas Constant.
3. Predict and measure the fastest way to cool a cup of hot water using heat transfer processes of conduction, convection, radiation and evaporation.
EQUIPMENT
Capstone, absolute pressure sensor, temperature sensor, syringe with tubing, quick-release coupling, metal canister with stopper, tubing-to-stopper connector, metal spoon, hot and cold water.
THEORY
The Ideal Gas Model predicts that when gases exert forces on the walls of their containers by means of the continual collisions with the surface, a pressure is produced. This Pressure depends on three parameters according to the kinetic-molecular model of ideal gases: Volume (m3), temperature (K), and the number of moles (mol) where pV = nRT. If one assumes that the Ideal Gas Law is valid at very low temperatures, the temperature where all atomic motion ceases to exist (i.e., where the pressure is zero), is called the Absolute Zero temperature (0K = −273.2 oC). Guillaume Amontons in 1700 ws the first to determine the Absolute Zero temperature, which we will redo his experiment using computer-based pressure and temperature measurements and extrapolate to when the pressure would be zero.
PROCEDURE
Part 1: Pressure vs. Volume
a. Connect the syringe to the Capstone’s absolute pressure sensor using the tubing and quick-release coupling. Set the initial syringe volume to 20.0 mL by disconnecting the sensor from the coupling, moving the piston to the 20 mL mark, and reconnecting.
b. Setup a pressure vs. time graph in Capstone and setup a data table with V(mL), 1/V(mL) and P(kPa). Measure the pressure at volume 20mL and record the pressure. Push the syringe’s plunger uniformly and slowly to 18mL and hold it there until the pressure reading is horizontal and constant. Repeat this process for 16, 14, 12, and 10 mL.
c. Plot P vs. 1/V and use a Trendline to display the equation. By looking at this plot, interpret it by answering the following questions (remember to use short concise sentences to explain your answers):
· Is the volume inversely proportional to the pressure? How does this support the Ideal Gas law?
· What kind of thermodynamic process is this: isobaric, isothermal, isochoric or adiabatic? What quantity is constant and what is its numerical value?
· Did the pressure change as expected when the volume was compressed from 20mL to 10 mL?
· The Ideal Gas Law implies that the intercept be zero. Does the displayed equation have a zero intercept? If not, explain if this is reasonable.
Part 2: Pressure vs. Temperature
a. Obtain from the physics staff the value of n/V for the day.
b. In Capstone, setup a pressure sensor to measure the pressure inside a canister (full of air) and a temperature sensor to measure the temperature of the water bath. Next, setup to plot pressure vs. temperature.
c. Starting with hot water (about 70-90oC), at the equilibrium pressure and temperature (constantly stirring) record the pressure and temperature. Add ice to cool the water by 5-10oC, re-measure the pressure and temperature again and repeat this process so that 10 data points are taken that span a temperature range of 50-90°C. Record your data in an Excel data table with T(oC) and p(kPa).
d. Plot p vs. T and display the line equation. From the slope, determine the Universal Gas Constant Rthy using the n/V value and determine the Absolute Zero temperature Tabs,thy where the pressure is zero.
e. Write your group’s prediction on the whiteboard and determine a class averages and uncertainties for (Rthy,class ± 2σR) and (Tabs,class ± 2σT). Are the accepted values, Raccepted = 8.31 J/mol∙K and Tabs,accepted = −273oC, consistent or inconsistent with a 2σ-confidence interval? Draw a distribution curve that clearly shows whether the accepted values fall within or outside the confidence interval.
Part 3: What is the fastest method to cool a cup of hot water, if your only available instrument is a spoon?
a. The only available equipment is a metal spoon, ice bath, beaker, Capstone thermometer, and access to hot water.
b. Try to have all three data runs start at the same starting temperature (to within a few degrees of each other). It will make analyzing your data much easier in the end.
c. First setup a reference curve to measure the temperature change of the hot water due to the heating of the environment (the air in the room). Setup a data table to measure the temperature every 30 seconds for 8 minutes.
d. Design two different experiments to get the largest change in temperature in 8 minutes. Rank your designs in terms of which method of cooling will be the fastest to slowest. Explain your reasoning using conduction, convection, radiation and evaporation.
e. Do the experiments by measuring the temperature every 30 seconds for 8 minutes for each prediction. (i) Plot your data on temperature vs. time graph such that all three runs are on a single plot. Make sure each data run is clearly labeled and that each plotted line has its own label and a different dashed line to differentiate between the three lines. (ii) Calculate and rank the absolute temperature differences (∆T ≡ |Tfinal – Tinitial|) for each of the three data runs from highest to lowest. (iii) Explain the temperature difference for the experiment using conduction, convection, radiation and evaporation.
Cooling water rules:
1. No other equipment other than what is listed may be used.
2. The only thing you can put in the hot water is the spoon and the temperature sensor. So this means
· No adding ice to the water.
· No putting the cup into an ice bath
· No pouring the water out of the cup
3. Cup must stay flat on table at all times.