An Introduction to Thermal Physics
1st Edition
ISBN: 9780201380279
Author: Daniel V. Schroeder
Publisher: Addison Wesley
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Chapter 5.3, Problem 52P
To determine
The variation of Van der Waals isotherm for
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Give the temperature T of 1 mole of ideal gas as a function of the pressure P, volume V, and the gas constant R and give the internal energy U of a rigid diatomic ideal gas as a function of its temperature T and the gas constant R.
Plot the van der Waals isotherm for T /Tc = 0.95, working in terms of reduced variables. Perform the Maxwell construction (either graphically or numerically) to obtain the vapor pressure. Then plot the Gibbs free energy (in units of NkTc) as a function of pressure for this same temperature and check that this graph predicts the same value for the vapor pressure.
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"
Chapter 5 Solutions
An Introduction to Thermal Physics
Ch. 5.1 - Prob. 1PCh. 5.1 - Consider the production of ammonia from nitrogen...Ch. 5.1 - Prob. 3PCh. 5.1 - Prob. 4PCh. 5.1 - Consider a fuel cell that uses methane (natural...Ch. 5.1 - Prob. 6PCh. 5.1 - The metabolism of a glucose molecule (see previous...Ch. 5.1 - Derive the thermodynamic identity for G (equation...Ch. 5.1 - Sketch a qualitatively accurate graph of G vs. T...Ch. 5.1 - Suppose you have a mole of water at 25C and...
Ch. 5.1 - Suppose that a hydrogen fuel cell, as described in...Ch. 5.1 - Prob. 12PCh. 5.1 - Prob. 13PCh. 5.1 - Prob. 14PCh. 5.1 - Prob. 15PCh. 5.1 - Prob. 16PCh. 5.1 - Prob. 17PCh. 5.2 - Prob. 18PCh. 5.2 - In the previous section 1 derived the formula...Ch. 5.2 - Prob. 20PCh. 5.2 - Is heat capacity (C) extensive or intensive? What...Ch. 5.2 - Prob. 22PCh. 5.2 - Prob. 23PCh. 5.3 - Go through the arithmetic to verify that diamond...Ch. 5.3 - Prob. 25PCh. 5.3 - How can diamond ever be more stable than graphite,...Ch. 5.3 - Prob. 27PCh. 5.3 - Calcium carbonate, CaCO3, has two common...Ch. 5.3 - Aluminum silicate, Al2SiO5, has three different...Ch. 5.3 - Sketch qualitatively accurate graphs of G vs. T...Ch. 5.3 - Sketch qualitatively accurate graphs of G vs. P...Ch. 5.3 - The density of ice is 917kg/m3. (a) Use the...Ch. 5.3 - An inventor proposes to make a heat engine using...Ch. 5.3 - Below 0.3 K the Slope of the 3He solid–liquid...Ch. 5.3 - Prob. 35PCh. 5.3 - Effect of altitude on boiling water. (a) Use the...Ch. 5.3 - Prob. 37PCh. 5.3 - Prob. 38PCh. 5.3 - Prob. 39PCh. 5.3 - The methods of this section can also be applied to...Ch. 5.3 - Suppose you have a liquid (say, water) in...Ch. 5.3 - Ordinarily, the partial pressure of water vapor in...Ch. 5.3 - Assume that the air you exhale is at 35C, with a...Ch. 5.3 - Prob. 44PCh. 5.3 - Prob. 46PCh. 5.3 - Prob. 47PCh. 5.3 - Prob. 48PCh. 5.3 - Prob. 49PCh. 5.3 - The compression factor of a fluid is defined as...Ch. 5.3 - Prob. 51PCh. 5.3 - Prob. 52PCh. 5.3 - Repeat the preceding problem for T/Tc=0.8.Ch. 5.3 - Prob. 54PCh. 5.3 - Prob. 55PCh. 5.4 - Prove that the entropy of mixing of an ideal...Ch. 5.4 - In this problem you will model the mixing energy...Ch. 5.4 - Suppose you cool a mixture of 50% nitrogen and 50%...Ch. 5.4 - Suppose you start with a liquid mixture of 60%...Ch. 5.4 - Suppose you need a tank of oxygen that is 95%...Ch. 5.4 - Prob. 62PCh. 5.4 - Everything in this section assumes that the total...Ch. 5.4 - Figure 5.32 shows the phase diagram of plagioclase...Ch. 5.4 - Prob. 65PCh. 5.4 - Prob. 66PCh. 5.4 - Prob. 67PCh. 5.4 - Plumbers solder is composed of 67% lead and 33%...Ch. 5.4 - What happens when you spread salt crystals over an...Ch. 5.4 - What happens when you add salt to the ice bath in...Ch. 5.4 - Figure 5.35 (left) shows the free energy curves at...Ch. 5.4 - Repeat the previous problem for the diagram in...Ch. 5.5 - If expression 5.68 is correct, it must be...Ch. 5.5 - Prob. 74PCh. 5.5 - Compare expression 5.68 for the Gibbs free energy...Ch. 5.5 - Seawater has a salinity of 3.5%, meaning that if...Ch. 5.5 - Osmotic pressure measurements can be used to...Ch. 5.5 - Because osmotic pressures can be quite large, you...Ch. 5.5 - Most pasta recipes instruct you to add a teaspoon...Ch. 5.5 - Use the Clausius–Clapeyron relation to derive...Ch. 5.5 - Prob. 81PCh. 5.5 - Use the result of the previous problem to...Ch. 5.6 - Prob. 83PCh. 5.6 - Prob. 84PCh. 5.6 - Prob. 85PCh. 5.6 - Prob. 86PCh. 5.6 - Sulfuric acid, H2SO4, readily dissociates into H+...Ch. 5.6 - Prob. 88PCh. 5.6 - Prob. 89PCh. 5.6 - When solid quartz dissolves in water, it combines...Ch. 5.6 - When carbon dioxide dissolves in water,...Ch. 5.6 - Prob. 92P
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- Compute the bulk modulus of an ideal gas, in terms of its pressure P, for both isothermal and adiabatic compressions.arrow_forwarddefine the chemical potential in terms of derivatives of the ĈE energy E and enthalpy H. For a one component system, these are u= ON and Evaluate these expressions for an ideal gas and compare to ON µ = -kT In (kT/PA³ ) from H=| P,s OF and |= 1 TP ON v.rarrow_forwardProvide 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?arrow_forward
- Show that the isothermal compressibility KT and the adiabatic compressibility KS of a Bose ideal gas are given by in the picture. where n(=N/V) is the density of the particles in the gas.arrow_forwardIn this problem you will investigate the behavior of a van derWaals fluid near the critical point. It is easiest to work in terms of reduced variables throughout. Still working in the same limit, find an expression for the difference in volume between the gas and liquid phases at the vapor pressure. You should find (Vg -Vi) ex: (Tc -Tl, where (3 is known as a critical exponent. Experiments show that (3 has a universal value of about 1/3, but the van der Waals model predicts a larger value.arrow_forwardWhen a liquid is compressed its Gibbs free energy is increased.To a first approximation the increase in the molar Gibbs free energy can be calculated by using (∂ ̄G/∂P)T= ̄V, assuming a constant molar volume.What is the change in molar Gibbs free energy for liquid water when it iscompressed to 1000 bar?arrow_forward
- You are studying a gas known as "gopherine" and looking in the literature you find that someone has reported the partition function for one molecule of this gas, 5/2 AzT q(V, T) = ) %3D h?m Assume that the molecules are independent and indistinguishable. Derive the expressions for the energy, (E), for this gas. Give your answers in terms of N, kg, T. V and the constants A and B. O (E) = NkaT ㅇ (E) =D NkaT ㅇ (E) %3D NkaT- O (E) = ANKET - O (E) = - T ㅇ (E)=D 쑤-arrow_forwardConsider a planetary atmosphere consisting of an ideal gas of atoms, each of mass m. The temperature T is regarded to be constant, independent of the height z above ground level. The acceleration of gravity g is constant, and the pressure at ground level is Po. Find the pressure as a function of z. (Hint: consider a thin slab of the atmosphere, and write and solve a simple differential equation.)arrow_forwardConsider phase transitions in conditions of variable pressure, volume and temperature. In the phase diagram for a single component system, the critical point defines the pressure, Pc, and temperature, Tc, at the end of the liquid-vapour co-existence line in P-T coordinates. A system consists of one mole of van der Waals gas, whose equation of state is P+ (V - b) = RT , where R is the universal gas constant. Using the information from (a) (ii), show that, for such a system, the molar volume at the critical point is given by V. = 3b. Show also that the other two parameters at the critical point are 8a and Pc Tc 27 Rb a 27b2arrow_forward
- Consider a Carnot engine operating between 75 degrees Celsius and 25 degrees Celsius using one mole of an ideal, diatomic gas. If V1 = 0.01 cubic meter and V2 = 0.10 cubic meter, answer the questions that follow. (C). What is qh (in Joules)? Express answer in THREE SIGNIFICANT FIGURES? (D). What is qc (in Joules)? Express answer in THREE SIGNIFICANT FIGURES? (E). What is the total work (in Joules)? Express answer in THREE SIGNIFICANT FIGURES?arrow_forwardUse the experimental value of the coefficient of viscosity for nitrogen (Table 16A.1) to estimate the collision cross-section of the molecules at 273 K.arrow_forwardUsing the same procedure to determine the fundamental equation of chemical thermodynamics (dG = –SdT + VdP) from the Gibbs free energy of a system (G = H – TS), can you please explain how to find the analogous fundamental equation for (A=U-TS)? Also, can you please handwrite the formula down instead of typing? I get confused with typed formulas sometime.arrow_forward
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