Help with 11 A graph of the speeds of air molecules in a sealed container is shown above. What11.)happens to the graph if the air is heated?Maxwell-Boltzmanndistributionspeed vAnswers:The peak of the graph remains in the same vertical position, but moves leftThe peak of the graph remains in the same vertical position, but Moves rightThe peak of the graph moves upThe peak of the graph moves downin a sealed container of gas is

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Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter17: Energy In Thermal Processes: The First Law Of Thermodynamics

Section: Chapter Questions

Problem 89P: Water in an electric teakettle is boiling. The power absorbed by the water is 1.00 kW. Assuming the...

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The Fahrenheit scale remains useful in part due to personal experience with temperature. For example, the average temperature range in a typical midlatitude city such as Gdansk, Poland (formerly Dansk, where Fahrenheit was born), is 25F to 78F over a year. a. Find the temperature range in Gdansk, Poland, in degrees Celsius and in kelvins. b. Many people say that 0F is a very cold day and 100F is an unpleasantly hot day. Convert these temperatures to the Celsius and Kelvin scales. c.When someone has an infection, her body may respond with a fever. A high fever (T 105F) can damage the brain. Convert this temperature to degrees Celsius.
In the chapter on fluid mechanics, Bernoulli's equation for the flow of incompressible fluids was explained in terms of changes affecting a small volume dV of fluid. Such volumes are a fundamental idea in the study of the flow of compressible fluids such as gases as well. For the equations of hydrodynamics to apply, the mean free path must be much less than the linear size of such a volume, adV1/3 . For air in the stratosphere at a temperature of 220 K and a pressure of 5.8 kPa, how big should a be for it to be 100 times the mean free path? Take the effective radius of air molecules to be 1.881011 m, which is roughly correct for N2.
What is the distinction between gas and vapor?
What would happen if the glass of a thermometer expanded more on warming than did the liquid in the tube? (a) The thermometer would break. (b) It could be used only for temperatures below room temperature. (c) You would have to hold it with the bulb on top. (d) The scale on the thermometer is reversed so that higher temperature values would be found closer to the bulb. (e) The numbers would not be evenly spaced.
Compare the SI units of specific heat and latent heat and explain any differences.
At a spot in the high Andes, water boils at 80.0C, greatly reducing the cooking speed of potatoes, for example. What is atmospheric pressure at this location?
How does the kinetic theory describe a gas?
Consider the Maxwell-Boltzmann distribution function plotted in Problem 28. For those parameters, determine the rms velocity and the most probable speed, as well as the values of f(v) for each of these values. Compare these values with the graph in Problem 28. 28. Plot the Maxwell-Boltzmann distribution function for a gas composed of nitrogen molecules (N2) at a temperature of 295 K. Identify the points on the curve that have a value of half the maximum value. Estimate these speeds, which represent the range of speeds most of the molecules are likely to have. The mass of a nitrogen molecule is 4.68 1026 kg. Equation 20.18 can be used to find the rms velocity given the temperature, Boltzmanns constant, and the mass of the atom or molecule. The mass of a nitrogen molecule is 4.68 1026 kg. vrms=3kBTm=3(1.381023J/K)4.681026kg=511m/s Using the results of Problem 28 and the rms velocity, we can calculate the value of f(v). f(vrms) = (3.11 108)(511)2 e(5.75106(511)2) = 0.00181 The most probable speed, for which this function has its maximum value, is given by Equation 20.20. vmp=2kBTm=2(1.381023J/K)(295K)4.681026kg=417m/s f(vmp) = (3.11108)(417)2 e(5.75106(417)2) = 0.00199 We plot these points on the speed distribution. The most probable speed is indeed at the peak of the distribution function. Since the function is not symmetric, the rms velocity is somewhat higher than the most probable speed. Figure P20.29ANS
Suppose a gasfilled incandescent light bulb is manufactured so that the gas inside the bulb is at atmospheric pressure when the bulb has a temperature of 20.0C. (a) Find the gauge pressure inside such a bulb when it is hot, assuming its average temperature is 60.0C (an approximation) and neglecting any change in volume due to thermal expansion or gas leaks. (b) The actual final pressure for the light bulb will be less than calculated in part (a) because the glass bulb will expand. What will the actual final pressure be, taking this into account? Is this a negligible difference?
A theoretical atmospheric lapse rate. Section 16.7 described experimental data on the decrease in temperature with altitude in the Earths atmosphere. Model the troposphere as an ideal gas, everywhere with equivalent molar mass M and ratio of specific heats y. Absorption of sunlight at the Earths surface warms the troposphere from below, so vertical convection currents are continually mixing the air. As a parcel of air rises, its pressure drops and it expands. The parcel does work on its surroundings, so its internal energy decreases and it drops in temperature. Assume that the vertical mixing is so rapid as to be adiabatic. (a) Show that the quantity TP (1 )/ has a uniform value through the layers of the troposphere. (b) By differentiating with respect to altitude y, show that the lapse rate is given by dTdy=TP(11)dPdy (c) A lower layer of air must support the weight of the layers above. From Equation 15.4, observe that mechanical equilibrium of the atmosphere requires that the pressure decrease with altitude according to dP/dy = g. The depth of the troposphere is small compared with the radius of the Earth, so you may assume that the free-fall acceleration is uniform. Proceed to prove that the lapse rate is dTdy=(11)MgR Problem 16.50 in Chapter 16 calls for evaluation of this theoretical lapse rate on the Earth and on Mars and for comparison with experimental results.
Water in an electric teakettle is boiling. The power absorbed by the water is 1.00 kW. Assuming the pressure of vapor in the kettle equals atmospheric pressure, determine the speed of effusion of vapor from the kettles spout if the spout has a cross-sectional area of 2.00 cm2. Model the steam as an ideal gas.
A high—pressure gas cylinder contains 50.13L of toxic gas at a pressure of 1.40107N/m2 and a temperature of 25.0C. Its value leaks after the cylinder is dropped. The cylinder is cooled to dry ice temperature (78.5C) to reduce the leak rate and pressure so that it can be safely repaired. (a) What is the final pressure in the tank, assuming a negligible amount of gas leaks while being cooled and that there is no phase change? (b) What is the final pressure it onetenth of the gas escapes? (c) To what temperature must the tank be cooled to reduce the pressure to 1.00 atm (assuming the gas does not change phase and that there is no leakage during cooling)? (d) Does cooling the tank appear to be a practical solution?