Please answer Analysis #3, 4, 5

4. According to any statistics text, one should, for statistically independent errors, add the squares of the uncertainties and take the square root of the result to arrive at the total uncertainty in the nal result. Brat: 91 +9 +eg+uuu 5. Look up the value for Lr in any reference (give the name) and compare with your value taking in account your total estimated uncertainty, em. Do they agree? (i.e. does em account for the difference between the calculated and theoretical values of L1?) Calorimetry Object: To determine the latent heat of fusion of ice and the latent heat of vaporization of steam; to do a full analysis of random and other errors which may affect the experiment; to discuss other possible systematic errors. REQUIRED EQUIPMENT: 1 vacuum ask triple beam balance (heavy capacity - 2610 g) ice cubes thermometer, clock steam generator with tubing, hot plate, etc. THEORY: Heat is a form of energy. How much energy does it take to raise the temperature of a body a given amount? How much energy does it take to change the phase of a substance? Calorimetry (the method of mixtures) can nd the answers to these questions. First we must dene the specic heat (capacity), c. The specic heat of a substance is dened as the amount of energy required to raise the temperature of one kilogram of the substance one degree Celsius or by the equation: Q=chT The latent heat, L is dened as the amount of heat required to change the phase of one kilogram of a substance with no change in temperature or by the equation: Q=mL (In our case, the phase changes are from ice to water and from water to steam; the latent heats are Lr and Lv respectively.) The fundamental principle under which calorimetry works is conservation of energy: for an isolated system, the total heat gained by a part of the system must be balanced by the heat lost by other parts of the system. Procedure: PART I - Latent Heat of Fusion 1. Dry the glass (inner) vacuum ask and weigh it. Record as me. 2. Place the ask in its plastic case and weigh the entire thermos. Record this value as m. 3. Fill the ask about 2;\"3 full of water at the highest temperature available from the tap. Weigh the ask again obtaining the quantity m2 . Mass of water present is mw = mg - m1. 4. Measure accurately T1, the initial temperature of the water. 5. Carefully add a handful of crushed ice to the ask. It might be necessary to dry the ice quickly with a paper towel if the ice appears wet. 6. Carefully stir with the thermometer and monitor the temperature. Record T2, the lowest temperature reached. (BEWARE: ensure that the ice has completely melted - if T; is close to 0 C, this may not be so.) 7. Weigh the entire ask (including water and melted ice). Record this value as m3. Then the mass of ice is m1: m3 - m2. PART 2 - Latent Heat of Vaporization 1. Fill the steam generator about 2/3 full with hot water and plug its top. If necessary, connect the thick rubber tubing to the side tube; place the steam generator on the hot plate. Plug in the latter and turn it to the maximum. 2. Dry the large vacuum ask. Place it in its plastic case and ll it about 4/5 full of cold tap water. Weigh the thermos and calculate the mass of water present as in part 1. 3. Allow the water and ask to come to thermal equilibrium and determine the temperature T1. 4. When steam is forming in the generator insert the rubber tubing well down into the vaCuum ask and hold it there for ab0ut ve minutes. [IMPORTANT See rst Question 2, below.] 5. Remove the tube, stir the water well and record temperature T2, the highest temperature reached. 6. Weigh the vacuum ask (including the water and condensed steam) and determine the mass of the condensed steam, ms. 7. Read the air pressure using a lab barometer and determine the boiling point of water, TB, by use of the tables in the Handbook of Physics. Part 1 Part 2 mo 370.9g w m1 568.3g m1 568.3g m2 1119.8g | m: 1228.1g 551.5 mw: m2- m1 659.8g T1 21.4C H13 1274.4 mg: m3- mg 46.3 TB 983C Analysis: PART 1 Latent Heat of Fusion 1. Determine nu, the effective mass of the glass ask in contact with the water. To do this, take 40% of mo. 2. Calculate the latent heat of fusion of the ice, Lf as follows: Heat gained by part of system = heat lost by the rest of system. If Q1 = m L2: heat gained by ice at 0 C changing to water at 0 C, Q2 = 1m cw (T2 - 0) = heat gained by melted ice going from 0 C to T2, and Q3 = (mg cc + mW cw) (T2 - T1) = heat gained by container and water in going 'om T1 to T2, (Note: Q3 is negative.) then, it follows that Q1 + Q2 + Q3 = 0 and one can solve for L1: For the heat capacities, use: cw = 4186 Jfkg-C (water), cc: 840 Jfkg-C (glass) 3. Estimate your errors and calculate their effect on the result as follows: a) Temperature readings: The thermometers are accurate to about i 04C. Increase (or decrease) T1 by this amount and recalculate Lr. Calculate the percent increase (or decrease) from the previous value of Lf. This is the uncertainty e1 in Lf due to uncertainty in the measurement of T1. Similarly, calculate the uncertainty e2 if Lf due to uncertainty in the measurement of T2. b) Measurement of mw; The beam balance is accurate to about i 0.1 g. Since the determination of rnW involves the equation mw = m2 - ml, increasing m2 and decreasing m. by 0.1 g could in effect increase mw by 0.2 g. Take the new value of mw, recalculate Lr and hence determine ea. 0) Measurement of Inc; We estimated that 40% of the glass was in thermal contact with the system and that therefore the effective mass me should be 40% of me. Perhaps 50% should have been used. Take the new value of Inc, recalculate Lr and hence determine e4. d) Measurement of mi: Since the determination of mi involves the equation m = m3 - m2, mi could in effect be increased by 0.1 3. Take the new value of mi, recalculate Lr and hence determine es. e) The specic heat of glass, cc: Differing values are given by various sources and c6 may be accurate to only 10%. Increase Cc by this value, recalculate Lr and hence determine e5. 0 The effect of the temperature probe: Suppose that the mass of the stainless steel probe in contact with the water is about 5 grams. Take the specic heat capacity of the probe to be around 0.1 caUg-C. Recalculate Lr taking into account the heat gained by the probe and hence determine e2. g) Other errors: There may be other errors, such as those involving the mass and specic heat capacity of the thermometer. Use your imagination and estimate any additional errors in Lr