According to the energy according to the equipartition theorem of degrees of freedom, what is the internal energy of 5 moles of rigid diatomic ideal gas molecules at equilibrium at temperature T?
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- An ideal gas has a pressure of 0.50 atm and a volume of 10 L. It is compressed adiabatically and quasi-statically until its pressure is 3.0 atm and its volume is 2.8 L. Is the monatomic, diatomic, or polyatomic?Under what circumstances would you expect a gas to behave significantly differently than predicted by the ideal gas law?The temperature of n moles of an ideal gas changes from T1 to T2 in a quasi-static adiabatic transition. Show that the work done by the gas is given by W=nR1(T1T2).
- A triatomic molecule can have a linear configuration, as does CO, (Figure a), or it can be nonlinear, like H,O (Figure b). Suppose the temperature of a gas of triatomic molecules is sufficiently low that vibrational motion is negligible. C H H (a) What is the molar specific heat at constant volume, expressed as a multiple of the universal gas constant (R) if the molecules are linear? Eint/nT = 2.5R (b) What is the molar specific heat at constant volume, expressed as a multiple of the universal gas constant (R) if the molecules are nonlinear? Eint/nT = 3R 1 At high temperatures, a triatomic molecule has two modes of vibration, and each contributes R to the molar specific heat for its kinetic energy and another R 2 for its potential energy. (c) Identify the high-temperature molar specific heat at constant volume for a triatomic ideal gas of the linear molecules. (Use the following as necessary: R.) Eint/nT = (d) Identify the high-temperature molar specific heat at constant volume for a…A triatomic molecule can have a linear configuration, as does CO2 (as shown), or it can be nonlinear, like H2O (as shown). Suppose the temperature of a gas of triatomic molecules is sufficiently low that vibrational motion is negligible. What is the molar specific heat at constant volume, expressed as a multiple of the universal gas constant, (a) if the molecules are linear and (b) if the molecules are nonlinear? At high temperatures, a triatomic molecule has two modes of vibration, and each contributes 1/2 R to the molar specific heat for its kinetic energy and another 1/2 R for its potential energy. Identify the high-temperature molarspecific heat at constant volume for a triatomic ideal gas of (c) linear molecules and (d) nonlinear molecules. (e) Explain how specific heat data can be used to determine whether a triatomic molecule is linear or nonlinear. Are the data as shown sufficient to make this determination?Consider the earth's atmosphere as an ideal gas of molecular weignt u in a uniform gravitational field. Let g denotc the acceleration due to gravity. (a) If z denotes the height above sea level, show that the change of atmos- pheric pressure p with height is given by dp where T is the absolute temperature at the height z. (6) If the decrease of pressure in (a) is due to an adiabatic expansion, show that dp Y dT Y -iT (c) From (a) and (b) calculate dT/dz in degrees per kilometer. Assume the atmosphere to consist mostly of nitrogen (N) gas for which y - 1.4. (d) In an isothermal atmosphere at temperature T, express the pressure p at height z in terms of the pressure po at sea level. (e) If the sea-level pressure and temperature are po and To, respectively, and the atmosphere is regarded as adiabatic as in part (b), find again the pressure p at height z.
- The only form of energy possessed by molecules of a monatomic ideal gas is translational kinetic energy. From kinetic, the average kinetic energy per molecule is KEmolecule = 3 2 kBT = 3 2 R NA T Use these results to show that the internal energy of a monatomic ideal gas at pressure P and occupying volume V may be written as U = 3 2 PV.A 0.825 mol sample of NO, (g) initially at 298 K and Molar heat capacity at constant volume (Cy,m) R Туре of gas 1.00 atm is held at constant volume while enough heat is applied to raise the temperature of the gas by 10.3 K. atoms Assuming ideal gas behavior, calculate the amount of heat linear molecules (q) in joules required to affect this temperature change and nonlinear molecules 3R the total change in internal energy, AU. Note that some where R is the ideal gas constant books use AE as the symbol for internal energy instead of AU. q = J AU = JAn ideal gas consists of 1.50 mol of diatomic molecules that rotatebut do not oscillate.The molecular diameter is 250 pm.The gas isexpanded at a constant pressure of 1.50*105 Pa, with a transfer of 200J as heat.What is the change in the mean free path of the molecules?
- A sample of 2.37 moles of an ideal diatomic gas experiences a temperature increase of 65.2 K at constant volume. Find the increase in internal energy if translational, rotational, and vibrational motions are possible.The temperature of 2.00 mol of an ideal monatomic gas is raised 15.0 K at constant volume.What are (a) the work Wdone by the gas, (b) the energy transferred as heat Q, (c) the change Eint in the internal energy of the gas, and (d) the change K in the average kinetic energy per atom?The best laboratory vacuum pump can generate a vacuum of about 1nTorr (10^-9 Torr). At 25°C and assuming that air consists of N_2 molecules with a collision diameter of 395 pm, calculate... (b) the mean free path,