Prob. 1: Laplace Law: thermodynamic properties of the interface between two phases are described by a state function called the surface tension σ. It is defined in terms of the work required to increase the surface area by an amount dA through dW = odA. By considering the work done against surface tension in an infinitesimal change in radius, show that the pressure inside a spherical drop of water of radius R is larger than outside pressure by 20/R. What is the air pressure inside a soap bubble of radius R?
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- One 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. `Provide an equation of state (relating pressure, volume and temperature) for a real gas and interpret the terms that take into account the differences between a real and ideal gas. Comment on the extreme limits (example:zero temperature). Under what conditions does the behavior of real gases conform to the behavior expected to ideal gases?I just need help with part D Problem 6: There are lots of examples of ideal gases in the universe, and they exist in many different conditions. In this problem we will examine what the temperature of these various phenomena are. Part (a) Give an expression for the temperature of an ideal gas in terms of pressure P, particle density per unit volume ρ, and fundamental constants. Answer: T = P/( ρ kB ) Part (b) Near the surface of Venus, its atmosphere has a pressure fv= 96 times the pressure of Earth's atmosphere, and a particle density of around ρv = 0.92 × 1027 m-3. What is the temperature of Venus' atmosphere (in C) near the surface? Answer: Tv = 490.55 Part (c) The Orion nebula is one of the brightest diffuse nebulae in the sky (look for it in the winter, just below the three bright stars in Orion's belt). It is a very complicated mess of gas, dust, young star systems, and brown dwarfs, but let's estimate its temperature if we assume it is a uniform ideal gas. Assume it is a…
- The Arhennius viscosity model describes how viscosity u depends on temperature 1: u = uo e E/RT 1 DVD DVD Here u is viscosity (Pa.s), I is the temperature (in "Kelvin), E is the activation energy (J mol¹), R is the universal gas constant (R = 8.3145 J mol¹¹ K¹) and U is a constant (Pa s). Ensure all your numerical answers are provided, accurate to 4 significant figures. Linearise this non-linear equation to allow the least squares fitting, i.e. write it in the form y = a + a₁x. Identify the independent (x) and dependent (y) variables and write the linearised equation in the answer boxes, clearly defining what ao and a₁ are equal to in terms of up, E and R. y: ao: a₁: X: IOHO OHO ManHi, could I get some help with this macro-connection physics problem involving moles and the Ideal Gas Law? The set up is: How many moles are there in a cubic meter of an ideal gas at 100 degree celsius (C) to 4 digits of precision with a pressure of 0.25 atm, assuming 1 atm = 101325 N/m2 with kB = 1.38e-23 J/K and NA = 6.022e23? Thank you.Problem 1: In statistical mechanics, the internal energy of an ideal gas is given by: N. aNkB 2/3 (3NKB U = U(S,V) = е where a is a constant. 1- Show that the variation of the internal energy is given by: 2 dS - \3V 2 dU = dV \3NkB 2- Using the fundamental relation of thermodynamic dU = T.ds – p. dV, show that the equation of state PV = nRT follows from the first expression of U.
- Figure I shows the P-V graph for a sample of a gas at 298 K. If this sample were heated to 312 K, this would be represented by a point 25. atm Figure 1 100 V/e 50 A At the top, left end of the line Off the line, above and to the right of it. B At the lower, right end of the line D Off the line, below and to the right of it.Solve 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.Please answer all parts: Problem 3: There are lots of examples of ideal gases in the universe, and they exist in many different conditions. In this problem we will examine what the temperature of these various phenomena are. Part (a) Give an expression for the temperature of an ideal gas in terms of pressure P, particle density per unit volume ρ, and fundamental constants. T = ______ Part (b) Near the surface of Venus, its atmosphere has a pressure fv= 91 times the pressure of Earth's atmosphere, and a particle density of around ρv = 0.91 × 1027 m-3. What is the temperature of Venus' atmosphere (in C) near the surface? Part (c) The Orion nebula is one of the brightest diffuse nebulae in the sky (look for it in the winter, just below the three bright stars in Orion's belt). It is a very complicated mess of gas, dust, young star systems, and brown dwarfs, but let's estimate its temperature if we assume it is a uniform ideal gas. Assume it is a sphere of radius r = 5.7 × 1015 m…
- Using 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"In the simple kinetic theory of a gas we discussed in class, the molecules are assumed to be point-like objects (without any volume) so that they rarely collide with one another. In reality, each molecule has a small volume and so there are collisions. Let's assume that a molecule is a hard sphere of radius r. Then the molecules will occasionally collide with each other. The average distance traveled between two successive collisions (called mean free path) is λ = V/(4π √2 r2N) where V is the volume of the gas containing N molecules. Calculate the mean free path of a H2 molecule in a hydrogen gas tank at STP. Assume the molecular radius to be 10-10 a) 2.1*10-7 m b) 4.2*10-7 m c) none of these.Given the ideal gas law P V = k T, where k> 0 is a constant. We have the equation for V in terms of P and T. Finding the rate of change of the volume with respect to temperature at constant pressure, the interpretation of the result is: 1 Because this partial derivative is negative, the volume decreases as the temperature decreases at a fixed pressure. . 2. Because this partial derivative is negative, the volume increases as the temperature increases at a fixed pressure. 3. Because this partial derivative is positive, the volume increases as the temperature decreases at a fixed pressure. 4. Because this partial derivative is positive, the volume increases as the temperature increases at a fixed pressure.