Gas molecules of mass m are confined in a cylinder of radius R and height L (with R >> L) kept vertically in the Earth's gravitational field. The average energy of the gas at low temperatures (such that mgL >> k,T ) is given by
Q: The RMS speed of a Hydrogen molecule (H2) at a temperature of 158°C is (in m/s):
A:
Q: Consider nitrogen gas in a container at temperature T = 245 K. A molecule’s average kinetic energy…
A: The mass of a mole of nitrogen is, m=28×10-3 kg/mol6.023×1023 /mol=4.649×10-26 kg The average…
Q: Suppose a Krypton atom (atomic mass = 83.8 u) near the surface of the Earth where the temperature is…
A:
Q: Consider a given volume of helium gas at room temperature (20.0 °C). [Molar mass of helium is 4.00 ×…
A: The answers are shown below.Explanation:
Q: Two gas cylinders are identical. One contains the monatomic gas argon (Ar), and the other contains…
A: MAr = 40 MKr = 84 Kinetic energy of atom = (3/2)kT = (3/2)(kPV/nR) = (3/2)(kPVMw/mR)
Q: A sealed container contains a fixed volume of a monatomic ideal gas. If the gas temperature is…
A: Hey, since there are multiple subpart questions posted, we will answer first three questions. If you…
Q: Two moles of an argon gas are at a temperature of 350 K. Calculate the average kinetic energy per…
A: number of moles (n) = 2 Temperature (T) = 350 kelvin
Q: 2.52 moles of an ideal gas are placed in a container whose volume is 8.17 x10−3 m3. The absolute…
A:
Q: Astronomers have recently discovered a new planet in a faraway solar system with a radius of roughly…
A: Given : Radius of the planet, R = 1211×103 m Atmospheric temperature, T = 562 °C = 835 K…
Q: A sample of argon gas is in a container at 35.0° C and 1.22 atm pressure. The radius of an argon…
A: An ideal gas is a theoretical gas made of point particles that are in random motion. The particles…
Q: A gas cylinder contains argon atoms (m = 40.0 u).. The temperature is increased from 293 K (20°C) to…
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Q: At atmospheric pressure and a temperature of 3.64 K helium can still exist in gas phase. Find the…
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Q: (a) An ideal gas occupies a volume of 2.4 cm3 at 20°C and atmospheric pressure. Determine the number…
A: The ideal gas equation is given by: PV=nRT, where P is pressure, V is volume, Tis temperature, and n…
Q: A gas is contained in a rigid container of constant volume; the pressure of the gas is also kept…
A: Given value--- the original rms speed of the gas molecules is 900 m/s . We have to find--- what…
Q: Much of the gas near the Sun is hydrogen nuclei. Its temperature would have to be 1.5 × 107 K for…
A: The root of the average of the molecular speed square is, Here, the root-mean-square speed is vrms,…
Q: An expensive vacuum system can achieve a pressure as low as 1.00 x 10-8 N/m² at 21.5 °C. How many…
A: Given, The volume, V= 1 cm3=1×10-6 m3 The temprature of vaccume system, T=21.5°…
Q: 20 C'eres is the largest asteriad in the Solar System. But witha mass of 9.38 x 10º kg, a radius of…
A: Given, T=-38.150CM=9.38×1020kgR=469.73 km
Q: Three moles of an argon gas are at a temperature of 305 K. Calculate the average kinetic energy per…
A: (a) Calculate the average kinetic energy per atom. KE=32kT =38.313052 = 3801.83 J Hence, the…
Q: For an ideal gas, O Cp = Cy for all ideal gases. O it depends on whether the gas is monatomic or…
A: For all ideal gas we have to find out the relationship between specific heat at constant pressure Cp…
Q: One mole of nitrogen has a mass of 28 g. Calculate the mean speed of the Maxwell-Boltzmann…
A: The mean speed of the Maxwell-Boltzmann distribution c = (8RT/(πM))1/2 M is molar mass R = 8.314…
Q: Consider nitrogen gas in a container at temperature T = 245 K. A molecule’s average kinetic energy…
A: Given: The temperature is T=245 K. The molecule’s average kinetic energy is Kavg=32kBT. The…
Q: An expensive vacuum system can achieve a pressure as low as 1.00 x 10-7 N/m² at 25.5 °C. How many…
A:
Q: - The escape speed from the Earth is 1.12 x 104 m/s, so that a gas molecule travelling away from…
A: As given, Escape speed from Earth, v=1.12×104 ms Average speed of a gas molecule is given by,…
Q: he rms speed of the molecules in 1.0 g of hydrogen gas is 1800 m/s . 400 J of work are done to…
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Q: Initially, the translational rms speed of a molecule if an ideal gas is 560 m/s. The pressure and…
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Q: Three moles of an argon gas are at a temperature of 275 K. Calculate (a) the kinetic energy per…
A: Part A:
Q: In the hot gases of an automotive engine's cylinders, temperatures may exceed 3100 k. What would be…
A: Given In the hot gases of an automotive engine's cylinders, temperatures may exceed 3100 k. The mass…
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- Consider a gas composed of 1 mol of deuterium atoms (molar mass = 2 g/mol) in a 0.025 m³ container at a temperature of 400 K. Using the results of statistical mechanics, calculate the Helmholtz energy of the gas in J.A particle on the surface of the Earth can "escape" the Earth's gravitation and continue to move away from the Earth forever, if it has a sufficient speed (called the escape speed). (a) Determine the escape speed (in m/s) if the particle is an oxygen molecule. Use 6.37 x 106 m for radius of the Earth. m/s (b) Determine the temperature (in K) at which the rms speed of the oxygen molecule is 13 times the escape speed. T = K (c) What If? The Universe is composed of 75% hydrogen and 25% helium by mass, yet these gases are not found in the Earth's atmosphere. Calculate the temperatures (in K) for which the minimum escape kinetic energy is nine times the average kinetic energy of hydrogen (H₂) molecules and helium atoms. K K TH2 THEHelium atoms interact very weakly with each other; helium only liquefies at 4.2 K at standardpressure. What is the kinetic energy of a helium atom:(a) at 100. K?(b) at 10.0 K?
- Three moles of an ideal gas are in a rigid cubical box with sides of length 0.300 m. (a) What is the force that the gas exerts on each of the six sides of the box when the gas temperature is 20.0°C?What is the RMS speed (in m/s) of a gas molecule, with mass 4.3x10-26 kg at a temperature of 98 degrees Fahrenheit?The mass of a helium atom is 6.650e–27 kg. What is the average speed of a helium molecule in a monoatomic gas at a temperature of 77 C?
- Long-term space missions require reclamation of the oxygen in the carbon dioxide exhaled by the crew. In one method of reclamation, 1.00 mol of carbon dioxide produces 1.00 mol of oxygen, with 1.00 mol of methane as a by-product. The methane is stored in a tank under pressure and is available to control the attitude of the spacecraft by controlled venting. A single astronaut exhales 1.21 kg of carbon dioxide each day. If the methane generated in the recycling of three astronauts' respiration during one week of flight is stored in an originally empty 155-L tank at −45.0°C, what is the final pressure in the tank? MPaTwo moles of a helium gas are at a temperature of 260 K. Calculate the average kinetic energy per atom, the root-mean-square (rms) speed of atoms in the gas, and the internal energy of the gas. HINT (a) the average kinetic energy per atom (in J) J (b) the root-mean-square (rms) speed (in m/s) of atoms in the gas m/s (c) the internal energy of the gas (in J) JMy Dyson vacuum cleaner can achieve a pressure as low as 10−8 Pa at 25C. How many molecules are there in a cubic centimeter at this pressure and temperature?
- At what temperature (in C) is the rms speed of helium atoms(molar mass 4.00 g/mol) the same as the rms speed of nitrogen molecules(molar mass 28.0 g/mol) at 20.0 C? (Note that helium remains agas at temperatures above -269 C.)A krypton-84 atom has a mass of 1.39 x 10-25 kg. (a) What temperature (in K) would a gas composed entirely of krypton-84 atoms have to be at in order for the rms speed of the atoms to equal the escape speed from Earth, 1.12 x 10 m/s? K (b) What temperature (in K) would a gas composed entirely of krypton-84 atoms have to be at in order for the rms speed of the atoms to equal the escape speed from the Moon, 2.37 x 10 m/s? KAn argon-40 atom has a mass of 6.64 ✕ 10−26 kg. (a) What temperature (in K) would a gas composed entirely of argon-40 atoms have to be at in order for the rms speed of the atoms to equal the escape speed from Earth, 1.12 ✕ 104 m/s? K (b) What temperature (in K) would a gas composed entirely of argon-40 atoms have to be at in order for the rms speed of the atoms to equal the escape speed from the Moon, 2.37 ✕ 103 m/s? K