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**Q1:**Academic Honesty Pledge I understand that students are expected to refrain from all forms of academic dishonesty as defined in the college policies and as explained and defined by college policies and procedures and directions from teachers or other college personnel. By signing this cover page I am confirming that the work presented here, including all the figures, tables, calculations, data and text, is mine and mine only. I hereby state that all work submitted in this report is mine and solely mine. Signature: Note: Only reports that include a signed cover sheet will be graded. 1 2 3 Objective of Evaluation Report presentation (must be typed) Observation and Analysis (Part I) Observation and Analysis (Part II) Total HCT PHY1203 PHYSICS II LAB 1 202210 Max. marks 5 65 30 100 Marks obtained 1 Objective: To determine the specific heat of a solid body. Background The specific heat of a substance is the quantity of heat necessary to raise a unit mass of the substance by a unit temperature difference. When a heat interchange takes place between two bodies initially at different temperatures, the quantity of heat lost by the hot body is equal to that gained by the cold body, and some intermediate equilibrium temperature is finally reached. This is true provided no heat is gained from or lost to the surroundings. In this case, we can apply the principle of conservation of energy. Heat lost by hot body = Heat gained by cold body Experimental setup and theory In this experiment, a solid sample of known mass (ml) is heated to a certain temperature near the boiling point of water (Ts). It is then quickly transferred to a calorimeter of known mass (mcal), which contains cold water of known temperature (Tw) and mass (mw). It should be assumed that temperature of calorimeter is the same as (Tw). When the solid sample and the calorimeter (including water) come to thermal equilibrium, the final temperature (T;) is noted. It is assumed that the heat loss to the thermometer is negligible and if the heat exchange with the environment is kept small, then the heat lost by the solid sample (-Qsol) is equal to the total heat gained by the calorimeter (Qcal) and the water (Qw). Thus, applying the principle of conservation of energy to our isolated system (the net heat gained by the system is zero): Q=mcAT Qw-Q sol+Qcal=0 W mwcw T-Tw-m sol sol Tsol-Tf+m calcat (T-Tw=0 W f W C sol mwcw Tf-Tw+mcal Ccal Tf-Tw W msol (Tsol-Tr If we ignore the heat gained by the calorimeter, the equation becomes: mw Cw Tf - Tw W C sol m sol T % error= sol Calculate the percentage error in experimental value - accepted value accepted value HCT PHY1203 PHYSICS II LAB 1 202210 × 100 (3) (1) (2) (5) (4) (6) 2 Apparatus: 0 0 0 0 0 000 Calorimeter Stirrer Thermometer Hotplate Metal sample Water Weighing scale Measuring cylinder Figure 1: Simulation of the specific heat capacity Experiment Experiment Step 5 300mL 200mL Run Demonstration 100ml LIQUIDS SOLIDS SOLUTIONS Unknown metal I Procedure and implementation 1. Follow the simulation link given below. Mass (g) Temp (°C) Show specific heat (J/g°C) 0.388 Overview Learning Outcomes Experiment Please choose one: HCT PHY1203 PHYSICS II LAB 1 202210 12.5 100. 20.92°C Run Experiment -600mL 500mL 400mL 300mL 200mL 100mL LIQUIDS Water - H₂O SOLIDS SOLUTIONS Mass (g) Temp (°C) XShow specific heat (J/g°C) 4.184 https://media.pearsoncmg.com/bc/bc_Omedia _chem/chem_sim/calorimetry/Calor.php 2. Click experiment and then run the experiment, as shown below. Chemistry Simulations: Calorimetry Click here 100. 20.0 RUN EXPERIMENT Then click here Show graph view Show microscopic view Replay 3. Then click on the solid and choose unknown metal 1. Also fix the mass of the solid (ms) and the temperature of the solid (Tl) to record in the table 1. This temperature is the initial temperature of the solid (Tsol). 4. Then click next to choose the liquid. Select water and fix the mass of the water (mw). Reset 3 5. Record the fixed initial temperature of the water (Tw) at around 20 °C. 6. Now click 'next' to run the experiment and wait until the system reaches to thermal equilibrium and record this temperature as the final temperature (T₁) Observation and Analysis (Part I) (20 marks) Enter your measurements into the following table. Remember to enter the correct units. Mass (…............ ..) Specific Heat c (J/g °C) Initial temperature T (…….........…... ..) Final temperature (............ ..) Metal Water 4.186 Table 1: Data collected with the metal, water and calorimeter. HCT PHY1203 PHYSICS II LAB 1 202210 1) Insert the screen shot of the system when it reaches the thermal equilibrium. marks) (5 2) Using equation (5), (considering only the water and metal), calculate the specific heat of the metal (ignore the heat loss due to calorimetry). You must show sufficient working to score full credit. (10 marks) 4 3) Determine which of the metals listed in the table (in appendix) has been used in this experiment. Give a justification for your choice. (5 marks) 4) Using equation (6), calculate the percentage error between the calculated value (in table 1 above) and the theoretical value of the specific heat of the solid metal used (refer to appendix). (5 marks) 5) Now use the same simulation link above and choose unknown metal 2 to enter your measurements into the following table. Remember to enter the correct units. marks) (20 Mass (…............ ..) Specific Heat c (J/g °C) Initial temperature T (.............….....) Final temperature (…....….... HCT PHY1203 PHYSICS II LAB 1 202210 .) Metal Water 4.186 5See Answer**Q2:**Condensed Matter 1) Obtain expressions for the heat capacity due to longitudinal vibrations of a chain of identical atoms; (a) in the Debye approximation; (b) using the exact density of states (Eq. below). With the same constants K and M, which expression gives the greater heat capacity and why? Show that at low temperatures both expressions give the same heat capacity, proportional to T. g(w) Hint: L (M\1/2 ла K &F sec (ka) 2N (4K 1/² - 0²) M 2) Estimate the Fermi temperatures of: (a) liquid ³He (density 81 kg m-³), and (b) the neutrons in a neutron star (density 10¹7 kg m−³). <-1/2 h² (3π²N\2/3 2m N(M¹/2 2(K/M)¹/2 T K (4K/M-²)¹/2 3) The Bragg angle for a certain reflection from a powder specimen of copper is 47.75° at a temperature of 293 K and 46.60° at 1273 K. Calculate the coefficient of linear thermal expansion of copper. 4) The crystal basis of graphene and of diamond is composed of two carbon atoms in nonequivalent position. Thus, their dispersion curves are composed of acoustical branches and optical branches and their acoustical branches are assumed to obey to the Debye approximation: = vs|k| and their optical branches are assumed to obey to the Einstein model @= @E = Cst. Deduce the numerical values of their Debye and Einstein temperatures from their crystal structure and their common sound. velocity, Vs = 18,000 m/s with also VE (Einstein frequency) at about 4 *10¹3 Hz. From the Cv graph shown in below, evaluate the specific heat of diamond at room temperature, 290 K. (h, kB) 100 75 50 25 0 C, (%) x 3;2;1 NkB unit 0 1D -2D -3D T/0₂ 1 Heat capacity, C, as a function of T/05 for 1D, 2D, and 3D solids. The vertical scale is in Nkg unit to multiply by 1, 2, or 3 as a function of the degree of freedom for the atom vibrations. Note the initial evolution in T, T2, or 73 as a function of the dimensionality of the solid. 5) (1) Knowing that lithium crystallizes in a cubic system with lattice considering its atomic mass (7) and its volumetric mass (546 kg⋅m-³), find which one is it ([simple cubic, body- centered cubic (bcc), or face-centered cubic (fcc)]? (2) Knowing that the valence electrons of this metal (1 per atom) behave as free electrons, find the shape of the Fermi surface and its expression and then calculate its characteristic dimension KF. (3) Compare KF obtained in (2) to the distance dm, which in reciprocal space separates the origin from the first boundary of the first Brillouin zone nearest the origin. (Evaluate dm using simple geometric considerations without having to sketch the first Brillouin zone.) (4) Find the Fermi energy of lithium EF, the Fermi temperature TF, and the speed of F of the fastest free electrons. (5) Knowing that the resistivity p of lithium is of the order 10-5 cm at ambient temperature, find the time of flight, t, and the mean free path A of conduction electrons. (6) Find the drift velocity vd of conduction electrons subject to a electric field of 1 V/m and compare it with the Fermi velocity VF. (7) Starting from the relation ke =1/3 CeVFA (or with the help of the Wiedemann-Franz expression), find the thermal conductivity due to electrons Ke of lithium at ambient temperature T = 300 K.See Answer**Q3:**2. (Target T1) While the simplicity of the ideal gas model makes it a good tool for understanding the foundation of many systems, this simplicity means it is not so useful when you need more precision. There are other models for real gases. One model gives the equation of state as N²o (P + №²a) (v (V-NB) = KT V2 where a and 3 are constants that depend on the molecules that make up the gas (specifically, a is related to the electrostatic interactions between molecules, and ß is related to the size of a molecule). Determine the work done by this gas on its surroundings as it expands from an initial volume Vo to a final volume 3V at a constant temperature To. Your result will be in terms of Vo, To, N, and constants.See Answer**Q4:**Partial Melt. If 2×105 J of energy in terms of heat is transferred to 3 kg of ice at 0 °C, how much ice melted in kg?See Answer**Q5:**Partial Melt. If 2x105 J of energy in terms of heat is transferred to 3 kg of ice at 0 °C, how much ice melted in kg?See Answer**Q6:**1. What is the total heat Q requires to melt a 2 kg ice at -5 °C to water at +10 °C ? Hint there is a phase change in the system. There are 3 separate Qs.See Answer**Q7:**7. An object is hung from scale and the reading is recorded to be 20 N. Then the object is completely immersed in water.What is the new scale reading if the object has a volume of 12.5x105 m². The density of water is 1000kg/m³ See Answer**Q8:**One considers the coupling of the orbital angular momenta of two p electrons. a) From the tables of the Clebsh-Gordan coefficients, give the explicit form of the following states: |L M> = |2 2>, 12 1>, |2 0>, |1 1>, |1 -1> et 0 0>. b) What can you say about the symmetry properties of the obtained states with respect to the exchange of the two electrons?See Answer**Q9:**Two moles of ideal mono atomic gas releases 6 000 J of heat when it is compressed by an external force. A 2 000J ofwork done on the gas during compression. 3. What is the change in the internal energy of the gas? 4. What is the change in the temp of the gas in Kelvin?See Answer**Q10:**a) What are the values of the quantum numbers S, L and J in the ground state of nitrogen? b) What are the angles between the total angular momentum , and the quantification axis z?See Answer**Q11:**5. An Aluminum rod is 20 cm long at 20 °C and has a mass of 350 g. If 10,000 J of thermal energy is added to the rod by heat, what is the change in the length of the rod in cm?See Answer**Q12:**2.One way to heat a gas is to compress it. When a certain gas under pressure of 2,000,000 Pa at 298.15 Kelvin is allowed to be compressed to 1/4 of its original volume, its final pressure is 3 times the initial pressure. What is its final temp?Hint use ideal gas law.See Answer**Q13:**6. A hot-air balloon has a volume of 2200 m². The basket, passengers and the balloon fabric (the envelope) weight 5,800 N,excluding the weight of heated gas in the envelope. If the balloon is floating in the air without accelerating upward or downward when the outside air density is 1.23 kg/m³, what is the average density of the heated gases in the envelope?See Answer**Q14:**Show from the Tables of the Clebsh-Gordan coefficients that the singulet and triplet states resulting from the coupling of the intrinsic spins of the two electrons of the He atom are indeed those given by the relations (II.23) and(11.24.11.25.11.26.) of the lecture notes.See Answer

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