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Derive the reduced expression for the compressibility factor z of a real gas; Explain in detail how the volume of the real gas at a given temperature and pressure can be determined using this mathematical expression and an appropriate graph.
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- Use the approximation 1 x-1 1 x x2 to determine an expression for the virial coefficient C in terms of the van der Waals constants.Perform a units analysis on the exponent of the barometric function and verify that the overall exponent is unitless.Determine the absolute pressure in torr exerted on an object submerged 1000 m below the surface of the sea. The density of sea water is 1020 kg/m³ and the acceleration due to gravity is 9.7 m/s². The local atmospheric pressure is 0.98 bar.
- In general, the compressibility factor Z tends to be larger than 1 at very high pressures (greater than 350 bar for methane.) Which Van der Waals' factor seems to be responsible for this behavior.--- a or b? ExplainDetermine the absolute pressure in torr on an object submerged 1000m below the surface of the sea. The density of sea water is 1020kg/m^3 and the acceleration due to gravity is 9.7 m/s^2. The local atmospheric pressure is 0.98 bar.Consider Argon (Ar) gas at a pressure of 1 bar and temperature of 300 K. The equivalent hardsphere radius (known as the Van Der Waal radius) of an Argon molecule is 188 picometers (pm)and its atomic mass is 39.948u. Note that 1u = 1.6605 x 10-27kg. a)How many molecules are contained in a cube 1 cm by 1 cm by 1 cm? b)Estimate the mean free path. At scales much larger than this, a continuum description holds. c)What is the density of the gas? d)Estimate the "root mean squared" molecular speed, i.e. SQRT( (V^2) ) e)Estimate the dynamic and kinematic viscosities. Compare these with literature values, forexample from webbook.nist.edu. f) Plot the variation of dynamic viscosity with temperature in the range between 300K and3000K at a fixed pressure of 1 bar. Use Matlab, Python, Mathematica, or any other softwareyou may choose.
- The density of air under normal conditions (temperature To-273 K, pressure po- 100 kPa) is 1.29 kg/ m3. Calculate the average molar mass of air.Compute the pressure difference between ‘m’ and ‘n’ as shown by the differential manometer in KPaIn general, the compressibility factor Z tends to be smaller than 1 at moderate pressures (around 150 bar for methane.) Which Van der Waals' factor seems to be responsible for this behavior.--- a or b? Explain
- A specially constructed velocity-selector accepts a beam of molecules from an oven at a temperature T but blocks the passage of molecules with a speed greater than the mean. What is the mean speed of the emerging beam, relative to the initial value? Treat the system as one-dimensional.Calculate the pressure exerted by 1.0 mol C2H6 behaving as a van der Waals gas when it is confined under the following conditions: (i) at 273.15 K in 22.414 dm3, (ii) at 1000 K in 100 cm3. Use the data in Table 1C.3 of the Resource section.Given that the density of air at 0.987 bar and 27°C is 1.146 kg m 3, calculate the mole fraction and partial pressure of nitrogen and oxygen assuming that a) air consists only of these two gases b) air also contains 1.0 mole per cent Ar. Please show step by step of calculations.