14. The volume of a body of gas is measured; the pressure is then computed from the formula p = k/v. If the allowable error in p is 0.001k, and the maximum error in measuring v is 0.06 cu. ft., what is the volume of the smallest container to which the process can be applied?
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- Find the number of molecule per unit volume of oxygen at N.T.P. (Mass of oxygen 5.313 × 1026 kg. R.M.S. speed of molecule = %3D oxygen molecules at N.T.P. = 461.2 m/s and 1 atmosphere pressure = 1.013 × 10° N/m²).A cylinder is filled with10.0Lof gas and a piston is put into it. The initial pressure of the gas is measured to be 268.kPa.The piston is now pushed down, compressing the gas, until the gas has a final volume of 8.70L. Calculate the final pressure of the gas. Round your answer to 3 significant digits.The pressure, P of an ideal gas, can be expressed as P = nRT/V where n is the number of moles, T is the temperature, V is the volume and R = 8.314JK^-1 mol^-1 is the ideal gas constant. a) Find the expression for deltaP in terms of deltan, deltaT and deltaV: deltaP = deltan + deltaT + deltaV b) Suppose that n = 1, V = 1m^3 and T = 300K initially. If n and V change to 9/5 and 7/10m^3 respectively, estimate the change in T(K) required to keep P constant.
- A cylinder is filled with 10.0L of gas and a piston is put into it. The initial pressure of the gas is measured to be 275.kPa .The piston is now pulled up, expanding the gas, until the gas has a final volume of 82.0L. Calculate the final pressure of the gas. Round your answer to 3 significant digits.Gold, which has a density of 19.32 g/cm3, is the most ductile metal and can be pressed into a thin leaf or drawn out into a long fiber a) If the sample of gold,with a mss of 27.63g, is pressed into a leaf of 2 um thickness, what is the area of the leaf? b)If instead,the gold is drawn out into a cylindrical fiber of radius 3 um , what is the lenght of the fiber ?Flow rate is expressed as gas velocity in cm/s. The gas is flowing through an open tubular column with an inner diameter of 0.25 mm. What volume flow rate (mL/min) corresponds to a gas velocity of 50 cm/s? (The volume of a cylinder is pr2 3 length, where r is the radius.)
- Assuming biological substances are 100% water, estimate the mass of a human kidney. Take a kidney to be roughly a sphere with a radius of 4 cm. kgThe specific reaction rate constant k is a strong function of temperature according to the following equation: 1 In the equation above, the reaction rate constant k is expressed in R is the universal gas constant 8.314- What is the unit of A? O mol m OK Om O J O mol K J mol 01 S Pa.m ³ m k=Axexp- Pa.m³ constant (1.314 P-²). mol. K E RT and T is the absolute temperature in K. The equation is dimensionally homogenous.Ideal gases are often studied at standard ambient temperature and pressure (SATP). The International Union of Pure and Applied Chemistry (IUPAC) defines SATP to be T = 25° C and P = 100 kPa. a. Calculate N/V (in particles per cubic meter) for an ideal gas at SATP b. How many atoms of an ideal gas at SATP are there in one cubic centimeter?
- 58. A retired partner from a large brokerage firm hasone million dollars available to invest in particularstocks or bonds. Each investment’s annual rate ofreturn depends on the state of the economy in thecoming year. The file P09_58.xlsx contains thedistribution of returns for these stocks and bonds asa function of the economy’s state in the coming year.As this file indicates, the returns from stocks andbonds in a fair economy are listed as X and Y. Thisinvestor wants to allocate her one million dollars tomaximize her expected value of the portfolio oneyear from now.a. If X 5 Y 5 15%, find the optimal investment strategy for this investor. (Hint: You could try a decisiontree approach, but it would involve a massive tree.It is much easier to find an algebraic expression forthe expected final value of the investment whena percentage p is put in stocks and the remainingpercentage is put in bonds.)b. For which values of X (where 10% , X , 20%)and Y (where 12.5% , Y , 17.5%), if any,…What is the pressure of the gas in the cylinder, in kPa (kiloPascal)? Pfluid = 13.9 × 10³ kg/m³, 1.0 atm = 1.00 × 105 Pa = 100 kPa, and g = 10.0 m/s². Your answer needs to have 3 significant figures, including the negative sign in your answer if needed. Do not include the positive sign if the answer is positive. No unit is needed in your answer, it is already given in the question statement. Pgas 16 cm -fluid 6.0 cmb) Each cylinder in a four-cylinder car engine has a bore diameter of 55.20 mm and the stroke for each piston is 127.50 mm. Calculate the cubic capacity of the engine in in cubic centimetres (cm³) and give your answer to two decimal places. c) For the engine mentioned in (b), the compression ratio, r, is 4.45 for the engine in, calculate the clearance volume per cylinder in in cubic centimetres (cm³) and give your answer to two decimal places.