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(a) Show that, for an ideal gas, the speed of sound given by Equation 14.9 can be written vsound =
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- A)An ideal gas is confined to a container at a temperature of 330 K.What is the average kinetic energy of an atom of the gas? (Express your answer to two significant figures.) B)2.00 mol of the helium is confined to a 2.00-L container at a pressure of 11.0 atm. The atomic mass of helium is 4.00 u, and the conversion between u and kg is 1 u = 1.661 ××10−27 kg.Calculate vrmsvrms. (Express your answer to three significant figures.) C)A gold (coefficient of linear expansion α=14×10−6K−1α=14×10−6K−1 ) pin is exactly 4.00 cm long when its temperature is 180∘∘C. Find the decrease in long of the pin when it cools to 28.0∘∘C? (Express your answer to two significant figures.)arrow_forwardUsing MATLAB editor, make a script m-file which includes a header block and comments: Utilizing the ideal gas law: Vmol= RT/P Calculate the molecular volume where: R = 0.08206 L-atm/(mol-K) P = 1.015 atm. and T = 270 - 315 K in 5 degree increments Make a display matrix which has the values of T in the first column and Vmol in the second column Save the script and publish function to create a pdf file from the script in a file named "ECE105_Wk2_L1_Prep_1"arrow_forwardThe volume V of an ideal gas varies directly with the temperature T and inversely with the pressure P. If a cylinder of 50 liters contains oxygen at a temperature of 200 K and a pressure of 5 atmospheres, what would the gas pressure be if the volume was changed to 30 liters and the temperature raised to 240 K?arrow_forward
- The ideal gas law relates the pressure P, volume V, and temperature T of an ideal gas: PV = nRT where n is the number of moles and R = 8.3145 J/(K mol). Plots of pressure versus volume at constant temperature are called isotherms. Plot the isotherms for one mole of an ideal gas for volume ranging from 1 to 10 m', at tempera- tures of T = 100, 200, 300, and 400 K (four curves in one plot). Label the axes and display a legend. The units for pressure are Pa. n=1arrow_forwardOne 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. `arrow_forwardA 0.75kg sample of gaseous monatomic Helium (He) has an rms velocity of 2500m/s in an insulated container of 0.8m3. a) What is the pressure of the gas? b) What is the temperature of the gas?arrow_forward
- The average translational kinetic energy for a molecule (Erans) is given by the following equation: Etrans =mv? Where m is the mass of the molecule and v? is the average of the square of the velocity. Given v2 = 3kT/m where k is the Boltzmann's constant, calculate the ratio of the kinetic energies at 200 °C and 100 °Carrow_forwardQ.5. One mole of oxygen gas is at a pressure of 6 atm and a temperature of27 °C. (a) If the gas is heated at constant volume until the pressure triples,what is the final temperature? (b) If the gas is heated until both the pressureand volume are doubled, what is the final temperature?arrow_forwardThe mean free path λ and the mean collision time T of molecules of a diatomic gas with molecular mass 6.00 x10^-25 kg and radius r=1.0x10^-10m are measured.From these microscopic data we can obtain macroscopic properties such as temperature T and pressure P? If yes, consider λ=4.32x10^-8m and T=3.00x10^-10s and calculate T and P.a)It's not possible.b)Yes,T=150K and P~2.04atm.c)Yes,T=150K and P~4.08atm.d)Yes,T=300K and P~4.08atm.e)Yes,T=300K and P~5.32atmf)Yes,T=400K and P~4.08atmg)Yes,T=400K and P~5.32atm.arrow_forward
- Compute the density in units of of an ideal gas under the following conditions: a) At and Torr pressure (1 Torr = 1mm Hg) this is called loschmidt number. b) In a vacuum of Torr at room temperature . This number is useful one for the experimentalist to know by heart. (10^-3 Torr = 1 micron)arrow_forward1. (a) Calculate a numerical value for the isothermal compressibility kT = -+ (), for air for summer in Albuquerque under the conditions of 0.83 atm and 311 K (100 °F), assuming ideal gas behavior. (b) The speed of sound is related to the isothermal compressibility via 1 Vsound p KT where the adiabatic exponenty = 7/5. Evaluate this expression to find the speed of sound in air (in meters per second, or in mph). It is helpful to note that the mass density p = (kg/mole) and molar density, i.e. the number of moles per cubic meter, which is the ratio n/V. You can use the ideal gas law PV = nRT to write the ratio n/V in terms of your known pressure P and known temperature T. The gas constant R = 8.314 J/(mole-Kelvin) or alternatively R = 0.08206 (liter-atm)/(mole- K). Standard temperature and pressure are 0 degrees C (273.15 K) and 1 atm (1.013×105 N/m²). A good estimate of M for air can be found by taking 20% of the molecular weight of oxygen and adding this to 80% of the molecular weight…arrow_forwardUse the Gibbs expression for entropy (eqn 14.48) to derive the formula for the entropy of mixing (eqn 14.40). Below are equations 14.48 and 14.40 - AS-NkB(x ln x + (1 − x) ln(1 - x)). = S = -kB Piln P¿. (14.40) (14.48)arrow_forward