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- Calculate the depth to which Avogadro's number of table tennis balls would cover Earth. Each ball has a diameter of 3.75 cm. Assume the space between balls adds an extra 25.0% to their volume and assume they are not crushed by their own weight.The temperature of atmosphere is not always constant and can increase or decrease with height. In a neutral atmosphere, where there is a significant amount of vertical mixing, the temperature decreases at a of approximately 6.5 K per km. The magnitude of be decrease in temperature as height increases is known as be lapse rate (I’). (The symbol is upper case Greek letter gamma.) Assume that be surface pressure is p0=1.013105Pa where T=293K and the lapse rate is (I=6.5Kkm) . Estimate the pressure 3.0 km above the surface of Earth.Repeat the preceding problem with 2.00 kg of ice instead of 1.00 kg.
- There are two important isotopes of uranium, U235 and U238 ; these isotopes are nearly identical chemically but have different atomic masses. Only U235 is very useful in nuclear reactors. Separating the isotopes is called uranium enrichment (and is often in the news as of this writing, because of concerns that some countries are enriching uranium with the goal of making nuclear weapons.) One of the techniques for enrichment, gas diffusion, is based on the different molecular speeds of uranium hexafluoride gas, UF6 . (a) The molar masses of U235 and U238F6 are 349.0 g/mol and 352.0 g/mol, respectively. What is the ratio of their typical speeds vrms ? (b) At what temperature would their typical speeds differ by 1.00 m/s? (c) Do your answers in this problem imply that this technique may be difficult?In winter, why did the pioneers store an open barrel of water alongside their produce?Some chimney pipes have a T-shape, with a crosspiece on top that helps draw up gases whenever there is even a slight breeze. Explain how this works in terms of Bernoulli’s principle.
- A gas follows on an isothermal curve, where p is the pressure, V is the volume, b is a constant, and c is a function of temperature. Show that a temperature scale under an isochoric process can be established with this gas and is identical to that of an ideal gas.(¦ Indicates a review question, which means it requires only a basic understanding of the material to answer. Questions without this designation typically require integrating or extending the concepts presented thus far.) . Is it possible to compress air without causing its internal energy to increase? If so, how?Compare the rate of heat conduction through a 13.0-cm-thick wall that has an area of 10.0 m2 and a thermal conductivity that of glass wool with the rate of heat conduction through a 0.750-cm-thick window that has an area of 2.00 m2, assuming the same temperature difference across each.
- The goal in this problem is to find the growth of an ice layer as a function of time. Call the thickness of the ice layer L. (a) Derive an equation for dL/dt in terms of L , the temperature T above the ice, and the properties of ice (which can leave in symbolic form instead of substituting the numbers). (b) Solve this differential equation assuming that at t=0 , you have L=0 . If you have studied differential equations, you will know a technique for solving equations of this type: manipulate the equation to get dL/dt multiplied by a (very simple) function of L on one side, and integrate both sides with respect to time. Alternatively, you may be able to use your knowledge of the derivatives of various functions to guess the solution, which has a simple dependence on t. (c) Will the water eventually freeze to the bottom of the flask?What effect does condensation on a glass of ice water have on the rate at which the ice melts? Will the condensation speed up the melting process or slow it down?Pouring cold water into hot glass or ceramic cookware can easily break it. What causes the breaking? Explain Pyrex, a glass with a small coefficient of linear expansion, is less susceptible.
