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Calcium carbonate,

(a) Which is stable at earth’s surface, calcite or aragonite?

(b) Calculate the pressure (still at room temperature) at which the other phase should become stable.

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# Chapter 5 Solutions

An Introduction to Thermal Physics

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- We're told oxygen is the most common element in the Earth's solid crust. But how much oxygen is there? Let's compare to the amount of oxygen in the Earth's atmosphere, like this: • The most common minerals in the Earth's crust are feldspars, and albite (NaAlSi,0g) is a typical feldspar. Let's assume the entire crust is made of albite with a density of 2.6 g/cm°. • The radius of the Earth is 6371. km and let's say the crust is the upper 100. km of it. • Let's model the Earth's atmosphere as a layer on top of the Earth about 100. km thick with an average density of 0.99 g/m", and which is 23.1% oxygen by mass. Use this information to calculate the ratio of the mass of oxygen in the Earth's atmosphere to the mass of oxygen in the Earth's crust. Round your answer to 2 significant digits.
*arrow_forward*2. Thermodynamics of growth and product formation. Starting with Equation 11.19, derive Equation 11.20 (case in which u is very large). YD(-mp) YP YD Yx YpYmax Yp. Ypp DX (11.19) 1 H+(-mp) Ymax DX YD Ypp (11.20) Yx(AGcatyn) 1+ YP YXG*arrow_forward*1. The expression for free energy as a function of temperature of a system with two states, one at energy 0 and other at 2e is A) F=-k T log(1-2B) F=-k Tlog(1+2) C) F=-k Tlog(1-²0¹²) D)F=-k Tlog(1+²) E) F = k₂Tlog(1+₂³) 2. For a gas of 'N photons having definite frequency w, the specific heat at constant volume is: A) Directly proportional to T C) Directly proportional to T B) Directly proportional to 7¹2 D) Stays constant E) Inversely proportional to T*arrow_forward* - A 101 gg -gg sample of steam at 100 ∘C is emitted from a volcano. It condenses, cools, and falls as snow at 0 ∘C. (For water, 80. cal (334 JJ) is needed to melt 1 gg of ice or must be removed to freeze 1 gg of water and 540 cal (2260 JJ) is needed to convert 1 gg of water to vapor at 100 ∘C∘C.). How many kilojoules of heat were released? Express your answer with the appropriate units.
*arrow_forward*3. Evaluate the following: ĵ· (21 – 3j + k) Solution and Answer: a. b. (2î – j) · (3î + k) Solution and Answer:*arrow_forward*Consider 1 g of sodium chloride that is successively divided into smaller cubes with various varying sizes as shown in table. Assuming a mass density of 2.178×10³ kg/m³ and surface energy of 2 × 10-5 J/cm², complete the table below and make your conclusion about how the total surface energy of 1 g of sodium chloride vary with particle size. Total surface area Side 0.1 cm 0.01 cm 0.001 cm 1 μm 1 nm Total Surface energy (J/g)*arrow_forward* - Can carbon dioxide be liquefied at room temperature ( 20ºC )? If so, how? If not, why not? (See Figure.) Figure: The phase diagram for carbon dioxide. The axes are nonlinear, and the graph is not to scale. Dry ice is solid carbon dioxide and has a sublimation temperature of – 78.5ºC .
*arrow_forward*A gas bottle contains 4.64×10²³ Hydrogen molecules at a temperature of 384.0 K. What is the thermal energy of the gas? (You might need to know Boltzmann's constant: kg = 1.38×10-23 J/K.) Submit Answer Tries 0/12 How much energy is stored in ONE degree of freedom for the whole system? Tries 0/12 What is the average energy of a single molecule? Submit Answer Tries 0/12 On average how much energy is stored by ONE degree of freedom for ONE single molecule? Submit Answer Tries 0/12 Submit Answer*arrow_forward*Consider an ideal gas at temperature T = 578 K and pressure p = 2 atm. Calculate the average volume per molecule in this gas in units of cubic nanometers (a nanometer is 10-9 m). Do not include units in your answer and state your answer as a number in normal form.*arrow_forward* - Helium is a very important element for both industrial and research applications. In its gas form it can be used for welding, and since it has a very low melting point (only 0.95 K under 2.5 MPa) it can be used in liquid form to cool superconducting magnets, such as those found in particle physics experiments. Say we have a cylinder of n = 105 moles of Helium gas at room temperature (T= 20° C). The cylinder has a radius of r = 16.5 cm and a height h = 1.31 m. What pressure (in kPa) is the helium gas under? P = Helium is usually kept in the highest pressure gas cylinders, which can typically withstand at least 500 atm of pressure. Would the tank in part (a) be able to maintain its structural integrity? In principle, these tanks could fail if the temperature of the Helium started rising - if they were stored in a hot environment, for instance. To determine how much of a danger this is, calculate the temperature (in C) the Helium gas would have to be to make the tank start to crack. Tmax
*arrow_forward*Helium is a very important element for both industrial and research applications. In its gas form it can be used for welding, and since it has a very low melting point (only 0.95 K under 2.5 MPa) it can be used in liquid form to cool superconducting magnets, such as those found in particle physics experiments. Say we have a cylinder of n = 85 moles of Helium gas at room temperature (T = 20° C). The cylinder has a radius of r = 12.5 cm and a height h = 1.51 m. A: What pressure (in kPa) is the helium gas under? B: In principle, these tanks could fail if the temperature of the Helium started rising - if they were stored in a hot environment, for instance. To determine how much of a danger this is, calculate the temperature (in C) the Helium gas would have to be to make the tank start to crack.*arrow_forward*Steady-state creep rate data are given here for some alloy taken at 200°C (473 K): ė, (h4) o (MPa) 2.4 × 10 3 53 2.7 × 10 2 71 If it is known that the activation energy for creep is 150000 J/mol, compute the steady-state creep rate at a temperature of 230°C ( 503 K) and a stress level of 46 MPa. h1 eTextbook and Media Save for Later Attempts: 0 of 3 used Submit Answer e to search a*arrow_forward*

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