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- Problem 1: Solve the one-dimensional heat equation ut = Upx for the completely insu- lated metal wire of unit length with the initial temperature given by u(x,0) = 6 sin?(7x) cos (Tx). (Tx) cos² (Tx). Find the equilibrium temperature inside the wire åfter long time.The total power emitted by a spherical black body of radius Rat a temperature T is P,. R Let P, be the total power emitted by another spherical black body of radius kept at 2 temperature 27T . The ratio, is (Give your answer upto two decimal places) P2One process for decaffeinating coffee uses carbon dioxide ( M=44.0 g/mol) at a molar density of about 14,0 mol/m3 and a temperature of about 60 . (a) Is CO2 a solid, liquid, gas, or supercritical fluid under those conditions? (b) The van der Waals constants for carbon dioxide are a=0.3658 Pa m6/mol2 and b=4.286105 m3/mol. Using the van der Waals equation, estimate pressure of CO2 at that temperature and density. `
- A mercury thermometer still in use for meteorology has a bulb with a volume of 0.780 cm3 and a tube for the mercury to expand into of inside diameter 0.130 mm. (a) Neglecting the thermal expansion of the glass, what is the spacing between marks 1 apart? (b) If the thermometer is made of ordinary glass (not a good idea), what is the spacing?Calculate the length of a 1-meter rod of a material with thermal expansion coefficient a when the temperature is raised from 300 K to 600 K. Taking your answer as the new initial length, find the length after the rod is cooled back down to 300 K. Is your answer 1 meter? Should it be? How can you account for the result you got?The product of the pressure and volume of a sample of hydrogen gas at 0.00 is 80.0 J. (a) How many moles of hydrogen are present? (b) What is the average translational kinetic energy of the hydrogen molecules? (c) What is the value of the product of pressure and volume at 200 ?
- One cubic meter (1 m³) of mono-atomic ideal gas, is initially at room temperature and atmo- spheric pressure. The mass of a single molecule is 1.34 × 10-26 kg. 1. Find the root mean square speed, vrms, Oof the molecules by equating the kinetic energy of a single molecule to its average thermal energy. 2. Knowing that the gas obeys the Maxwell speed distribution 3/2 4nv²e-2T m mu2 D(v) = (0.2) 2πkT such that D(v)dv = 1. (0.3) Find the expression of the probability (do not do the integral) that a particular molecule is moving with a speed faster than 2000m/s. 3. The gas is heated at constant pressure until it triples in volume. Calculate the increase in its entropy.A monatomic ideal gas undergoes an isothermal expansion at 300 K, as the volume increased from 0.020 to [2*v1] m³.The final pressure is 120.61kPa. The ideal gas constant is R = 8.314 J/mol · K. %3D What is the heat transfer Q to the gas in kilojoules? Please enter your numerical answer with two decimal places. (for example for 2090 J, enter 2.09 )1.7 Ideal gas response functions Find the thermal expansion coefficient and the isothermal compressibility for an ideal gas and show that in this case Cp - Cy = - a² can be reduced to Cp – Cy = Nkg for the molar specific heats. TV Кт
- 8. AN gases at STP because behave as id cal gases a.j The T and aoat STP are 273k and latm b.) The ideal gas formu1a onsiders the ir moucular weight C- Jthe velocitics are very fast and their intrinsic motecular propertics beome negligible OF the e :) hore abo ve1. The figure shows the natural loga- rithm of the particle density of air (p = 1.225 kg m-3 at h = 0) for a constant temperature. Given that the linear fit to the data is In(n) = 58.533 at h = 0 and In(n) 57.386 at h = 10ª m, stating any assumptions used, 10 2000 4000 6000 8000 Height, h [m] (a) calculate the average mass of an air particle, (b) determine the temperature of the air. Number density, In(n) [m] 57.5 58 58.5Solve the common pressure and temperature assuming no heat loss in the containers and the surrounding of the two containers A and B that hold an ideal gas at pressure PA and PB, and absolute temperature TA and TB respectively. The containers are connected by a thin tube (and a close valve). The valve is opened to allow the pressures and temperatures to equalize.