[12 pts] A two-dimensional gas of molecules, each of mass m, is in thermal equilibrium at...
Suppose you had an ideal gas of molecules of mass m that can move only in one dimension. The gas is in thermal equilibrium at a temperature T. Wnte an expression proportional to the probability of finding a molecule with velocity i. bive an expression Diy fortheprobablity density for molecules of speed v in the gas. Hint: this is much easier to derive than in the three dimensional case. For each v how many speeds vare possible in one dimension?...
The speed of a molecule in a uniform gas at equilibrium is a random variable V whose density function is given by where and k, T and m denote Boltzmann’s constant, the absolute temperature, and the mass of the molecule, respectively. (a) Derive the distribution of , the kinetic energy of the molecule. (10) (b) Find E (X). (4) f(v) = arre-buv > 0,
A box contains 104 gas molecules, 2500 of nitrogen and 7500 of argon in thermal equilibrium. The molecular weight of N2 is 28g/mol, and of Ar is 40g/mol. The total thermal energy of the collection of 104 molecules is 5x10-17J. What is the temperature of this gas? T =
At what temperature would the root-mean-square speed (thermal speed) of oxygen molecules be 116 m/s? Assume that oxygen approximates an ideal gas. The mass of one O2 molecule is 5.312 x 10-26 kg. The Boltzmann constant is 1.38 × 10-23 J/K.
(4) (24 pts): A gas of nitrogen, N2, is in thermal equilibrium. a) The average kinetic energy of a molecule of N2 is mVrms/2. Assume N2 to be a diatomic gas with only three activated degrees of freedom. Write an expression for Vrms as a function of the temperature. b) Assume T = 20 °C. Compare Vrms to the escape velocity of a molecule from the surface of the Earth. Explain whether we need to worry that Earth might lose...
3. Consider a hypothetical non-ideal gas of particles confined to exist along a line in one dimension. The particles are in thermal equilibrium but due to their complex interactions the velocity distribution function is not Maxwellian, but rather has the form: where C and vo are constants. Note that v is the velocity (not the speed) and can take on negative values. Express your answers below in terms of vo- a. Solve for the constant C b. Draw a sketch...
Consider a gas of N molecules of mass m, occupying a volume V at temperature T and characterized by a fugacity f(T, V, N)--יג, where-2TmRT bound to a surface that has a total of No. The partition function of the bound gas molecules is Ž(T) At equilibrium, some of these molecules are a and only depends on T since gas molecules are bound to the surface. Using the grand canonical ensemble, find the ave to zero and the temperature is...
Consider gas molecules in the earth's atmosphere which obey the Maxwell speed distribution law, m 3/2 P(v) = 41 27 KT 2KT Here m is the mass of the molecule, v is the speed and k is Boltzmann's constant. (a) Find the temperature T, such that the most probable speed is sufficient to escape the earth's gravitational pull. (b) What is this temperature for hydrogen gas?
Suppose that the root-mean-square velocity Us of water molecules (molecular mass is equal to 18.0 g/mol) in a flame is Feedback found to be 1170 m/s. What temperature does this represent? The root-mean-square velocity Urms of a molecule in a gas is related to 5.95 x109 temperature the mass of the molecule m and the temperature of the gas T. 3KT Urms The Boltzmann constant is k = 1.38 x 10-23 J/K.
The ammonia molecule (NH3) has a dipole moment of 5.0×10−30C⋅m. Ammonia molecules in the gas phase are placed in a uniform electric field E⃗ with magnitude 1.0×106 N/C . A)What is the change in electric potential energy when the dipole moment of a molecule changes its orientation with respect to E⃗ from parallel to perpendicular? B) At what absolute temperature T is the average translational kinetic energy 32kT of a molecule equal to the change in potential energy calculated in part...