In Section 18-1 we assumed the gas molecules made perfectly elastic collisions with the walls of the container. This assumption is not necessary as long as the walls are at the same temperature as the gas. Why?
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3. In Section 18-1 we assumed the gas molecules made perfectly elastic collisions with the walls of the container. This assumption is not necessary as long as the walls are at the same temperature as the gas. Why?
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- If He gas has an average kinetic energy of 4070 J/mol under certain conditions, what is the root mean square speed of O2 gas molecules under the same conditions?I am given the following information: "A 700 kg piston is initially held in place by a removable latch above a vertical cylinder. The cylinder has an area of 0.1 m^2; the volume of the gas within the cylinder initially is 0.1 m^3 at a pressure of 10 bar. The working fluid may be assumed to obey the ideal gas equation of state. The cylinder has a total volume of 0.25 m^3, and the top end is open to the surrounding atmosphere at 1 bar." (a) Assume that the frictionless piston rises in the cylinder when the latches are removed and the gas within the cylinder is always kept at the same temperature. This is an odd assumption, but provides approximate results that are easy to obtain. What will be the velocity of the piston as it leaves the cylinder. (b) What will be the maximum height to which the piston will rise? (c) What is the pressure behind the piston just before it leaves the cylinder? (d) Now suppose the cylinder was increased in length such that its new total volume is 0.588 m3.…2. Consider a monatomic gas in a 2-dimensional box with a rectangular area A. The velocity distribution for this gas is given by (you do not need to prove this): {-m (C +C)/ 2kT} f (C,,C,)=A e Find: A, the speed distribution, and the mean speed, C.
- What is the average translational kinetic energy of an ideal-gas molecule at 27 C? (b) What is the total random translational kinetic energy of the molecules in 1 mole of this gas? (c) What is the rms speed of oxygen molecules at this temperature?suppose you have 7 moles of nitrogen gas at 310 K. a) What is the average translational kinetic energy of a gas molecule at this temperature? b) Find the rms speed pf a molecule at this temperature?At what temperature does the rms speed of a nitrogen molecule and a hydrogen molecule equal the escape speed from the Earth’s surface? You’ll find that these temperatures are very high, so you might think that the Earth’s gravity could easily contain both gases. But not all molecules move with vrms. There is a distribution of speeds, and a small percentage of molecules have speeds several times vrms. Bit by bit, a gas can slowly leak out of the atmosphere as its fastest molecules escape. A reasonable rule of thumb is that the Earth’s gravity can contain a gas only if the average translational kinetic energy per molecule is less than 1% of the kinetic energy needed to escape. Use this rule to show why the Earth’s atmosphere contains nitrogen but not hydrogen, even though hydrogen is the most abundant element in the universe. Repeat this calculation for the Moon. Would you expect the Moon to have an atmosphere? Explain
- If all the gas particles are in a state of moving toward each other and causing a collision, then the calculated velocity is... A. The most possible speedB. Average speedC. Mean square root velocityD. Relative speedE. Speed squareda) Estimate the average spacing between the molecules of 1 mol of an ideal gas at a pressure of 1atm and a temperature of 300 K. b) 1 mol of liquid water occupies a volume of 18 cm. Estimate the spacing between molecules. c) Use your result from part (a) to estimate the diameter of a water molecule. d) Estimate the factor by which water expands when it boilsTwo containers hold an ideal gas at the same temperature and pressure. Both containers hold the same type of gas, but container B has twice the volume of container A. (i) What is the average translational kinetic energy per molecule in container B? (a) twice that of container A (b) the same as that of container A (c) half that of container A (d) impossible to determine (ii) From the same choices, describe the internal energy of the gas in container B.
- A 7.00-L vessel contains 3.50 moles of gas at a pressure of 1.60 × 106 Pa. Find (a) the temperature of the gas and (b) the average kinetic energy of the gas molecules in the vessel. (c) What additional information would you need if you were asked to find the average speed of the gas molecules?The density of helium gas at 0°C is po = 0.179 kg/m³. The temperature is then raised to T = 160°C, but the pressure is kept constant. Assuming that helium is an ideal gas, calculate the new density p, of the gas. kg/m³The temperature of an ideal monatomic gas is increased from 25 C to 50 C. Does the average translational kinetic energy of each gas atom double? Explain. If your answer is no, what would the final temperature be if the average translational kinetic energy was doubled?