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- Phys 372 Assignments

P int 8 4 x 10 4 Pa Ignoring any other systems what problem can you foresee a calculation is required 2 How good is the bedspring model for a solid To find out evaluate C P for copper ρ 8 92 g cm 3 at room temperature for which equations were given in class and for which 19 on the phy372 home page will be useful Compare your result to the measured value 18 on home page and comment on the result 3 Do Prob 1 51 in the text H 2 O is in liquid form Calculate the mass of a mole of glucose to help visualize the quantity of this sugar Convert your result to calories see text inside front jacket and then to the calories that are normally used for measurements of human activity and weight Finally calculate the number of calories per gram for this sugar Check that the result is about the correct value for a sugar providing your reference internet is okay 4 Do Prob 2 3 in the text 5 The spin of an electron of hydrogen in its ground state can be either parallel or anti parallel to the spin direction

Original URL path: http://www.astro.queensu.ca/~irwin/phy372/y2015/assignment4.html (2016-02-13)

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deducted for assignments that are not clear Worksheets must not be shared between students 1 In class I showed how you would find an expression for the multiplicity of an Einstein solid in the high temperature limit Follow a similar procedure to find a simple expression for the multiplicity of an Einstein solid in the low temperature limit Ensure that your steps are clear and that you indicate what if any approximations or assumptions are involved 2 Read the Entropy of Mixing section in the text p 79 and do prob 2 37 3 Do prob 3 11 in the text 4 Starting with the first TdS equation expressed in terms of the coefficients β κ and C V i e Eqn 1a of 24 on the web page show that for isentropic expansion or contraction of an ideal gas the result reduces to Eqn 1 39 in the text 5 The pressure on a block of copper at a temperature of 0 Celsius is increased isothermally from 1 atm to 1000 atm Assume that the parameters β 5E 5 K κ 8E 12 m 2 N and the density ρ 8 9E3 kg m 3 are approximately constant during

Original URL path: http://www.astro.queensu.ca/~irwin/phy372/y2015/assignment5.html (2016-02-13)

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and draw this Carnot cycle on a the VT plane b the PT plane and c the UT plane with points labelled and arrows shown Let the second thermodynamic coordinate represent the x axis e g VT means T as the x axis Ensure that the curvature is clear where relevant 2 Do Prob 4 18 in the text 3 Do Prob 4 22 in the text From those results do problem 4 26 in the text 4 Air flows into a gasoline engine at 95 kPa and 300 K The air is then compressed with a volumetric compression ratio of 8 1 The combustion process releases 1300 kJ kg of energy as the fuel burns Find the temperature and pressure after combustion The working substance is well approximated as air with a specific heat of c V 717 J kg K 5 An air conditioner operates on 800 W of power and has a coefficient of performance of 2 80 with a room temperature of 21 0 0 C and an outside temperature of 35 0 0 C a Calculate the rate of heat removal for this unit b Calculate the rate at which heat is discharged to the

Original URL path: http://www.astro.queensu.ca/~irwin/phy372/y2015/assignment6.html (2016-02-13)

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is given by u 3 2 RT a v Show that the molar enthalpy is given by h T v 5 2 RT RTb v 2a v where a and b are the usual van der Waals constants and v is the molar volume b It can be shown that the Joule Thomson coefficient for such a gas is given by μ T P h 1 c P RTv 3 b 2av v b 2 RTv 3 2a v b 2 where c P is the molar specific heat at constant pressure Find an expression for the inversion temperature T inv for this gas The right hand side will include only v and constants c For N 2 a 0 1408 J m 3 mol 2 and b 3 913 x 10 5 m 3 mol and let v 1 27 x 10 4 m 3 per mole What is the inversion temperature d What pressure do these values of v and T correspond to Check your result against the inversion curve given in 30 on the Phy 372 home page e Suppose b inv Recalculate T inv for N 2 for that case Do you find something similar to

Original URL path: http://www.astro.queensu.ca/~irwin/phy372/y2015/assignment7.html (2016-02-13)

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A is a function of T only Determine the following quantities expressing all extensive quantities in molar specific form expressing the results in terms of known quantities and constants and presenting the results as simply as possible a the equation of state b the entropy s c the other thermodynamic potentials h f and u d the molar specific heats c v and c p e the volume expansion coefficient β and isothermal compressibility κ T f the Joule Thomson coefficient μ 3 A container with total volume V is divided into 3 partitions containing respectively 1 kmole of He 2 kmole of Ne and 3 kmole of Ar all gaseous Each compartment is at T 300 K and P 2 atm The partitions are then removed and the gases diffuse together with no change in temperature Find a the final fraction by number of each gas b the final partial pressures of each gas c the change in the Gibbs free energy Δ G d the change in the entropy Δ S 4 In class I indicated that there was a region on the equation of state surface at which the properties of a dense gas become essentially the properties of a liquid without precipitation occurring It should be possible then to define a single equation of state that describes both the liquid and gas phases of a substance for that region The van der Waals model is such an example Figure 5 20 in the text shows isotherms in the P V plane for a van der Waals gas plotted in terms of the critical pressure P c and the critical volume V c see page 184 text Note that there is a unique point on this plot for which both the first and second derivatives are zero

Original URL path: http://www.astro.queensu.ca/~irwin/phy372/y2015/assignment8.html (2016-02-13)

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a mean value of about 30 MPa km At a depth of 50 km will it be more likely that albite or jadeite quartz would form Explain 2 Do Probs 6 6 and 6 7 in the text 3 This question is based on Prob 6 18 in the text a Do the first part of Prob 6 18 showing how Z can be used as a generating function to obtain the mean value of E 2 i e derive the first equation in the problem b Write the quantity σ E 2 for which you have an expression in your notes in terms of Z and its derivatives with respect to β c Now write the specific heat at constant volume C V U T V with a change of variables so that it is expressed in terms of a partial of U with respect to β rather than T d Since you know how U can be generated from Z see notes it is now possible to carry out the differentiation to find an expression for C V in terms of Z β and constants Write the final result for C V in terms of σ E 2

Original URL path: http://www.astro.queensu.ca/~irwin/phy372/y2015/assignment9.html (2016-02-13)

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NO LATE ASSIGNMENTS WILL BE ACCEPTED no not kidding not even five minutes late 1 Starting with the Helmholtz Function for a monatomic ideal gas derive Eqn 2 49 2 Do Prob 7 20 in the text 3 Do Prob

Original URL path: http://www.astro.queensu.ca/~irwin/phy372/y2015/assignment10.html (2016-02-13)

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other is a mm wave project The European project is the LSA while the American project is the MMA These may be combined into one project called ALMA Using the web sites http www ras ucalgary ca SKA and http iram fr LSA as starting points write a 2 page summary of these projects Canada can afford to be involved in only one of them In your last paragraph if

Original URL path: http://www.astro.queensu.ca/~irwin/phy415/assn1.html (2016-02-13)

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