The temperature, at which the root mean square velocity of hydrogen molecules equals their escape velocity from the earth, is closest to: [Boltzmann Constant, kg = 1.38 × 1023 J/K Avogadro number, NA = 6.02 x 1026/kg Radius of Earth: 6.4 x 106 m Gravitational acceleration on Earth = 10 ms2]
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- What is the root mean square velocity, vrms, for Helium atom (He) at 66oC? Hint: How many amu does an He atom contain? 1 amu = 1.67 x 10-27 kg Boltzman's Constant, k = 1.38 x 10-23 J/K Give your answer in m/s to 4 significant figures (NO DECIMALS)What is the average thermal velocity of a hydrogen molecule H at 27 \deg C? (Assume: Boltzmann constant = 1.38 x 10-23 J/K and the mass of H is m = 3.32 x 10-27 kg)In the question its asks for the rate of energy transfer P after you find what the interface temperature T is. Upon completion from submitting T in into the intial rate equation the final expansion gives: P = A(Th - Tc) / (L1/ k1) + (L2/ k2) I understand how T was achieved from expanding the P1 = P2 substitution, but how is P found from inserting T into P1 = k1A (T - Tc / L1)?
- Derive Kelvin’s formula and the maximum free energy formula: rd* = 2 σLV /nL RT ln S ΔG = 16 π σLV^3 / 3 (nL RT ln S)^2 where σLV =surface tension, nL = moles of liquid water per unit volume, R = universal gas constant, T = temperature S = supersaturation pure liquid water = e/es(T) : e = water vapor partial pressure The first equation can also be rearranged to give an expression for the supersaturation, S: ln S = 2 σLV /nL RT rd* or S = exp(2 σLV /nL RT rd*)The escape speed from the Moon is much smaller than from Earth and is only 2.38 km/s. At what temperature would bromine molecules (with a molecular mass equal to 159.8 g/mol) have an average speed vrms equal to the Moon's escape speed?the partition function of an ideal gas of diatomic molecules in an external electric field & is [g(V, T, 8)]" Q(N, V, T, 8) N! where (2mmkT 312 (87 IkT -hv/2kT e q(V,T, 8)= V{ h2 (kT' (µ8 sinh kT) h2 (1 – e-hv/kT) Here I is the moment of inertia of the molecule; v is its fundamental vibrational frequency; and u is its dipole moment. Using this partition function along with the thermodynamic relation, dA = -S dT –p dV – M de where M=Nū, where u is the average dipole moment of a molecule in the direction of the external field &, show that kT] coth kT, Sketch this result versus & from & =0 to & =∞ and interpret it.
- The average thermal energy for a mono-atomic gas is: (kB is Boltzmann constant and T, absolute temperature) kBT kBT kBTWhat is the probability that an O2 molecule in a sampleof oxygen at 300 K has a speed between 5.00 × 102 and5.10 × 102 m s-1 ? (Hint: Try approximating the area underthe Maxwell–Boltzmann distribution by small rectangles.)Suppose a gas of 87 Rb atoms is trapped in an atomic trap. If the average separation between nearest neighbour atoms in the trap is approximately (a) 100 times or (b) 10 times the atomic radius (265 pm), find the temperature at which you would expect Bose-Einstein condensation to occur. Make the same calculation for 23 Na (atomic radius 190 pm). Give your answers in Kelvin.
- The escape velocity of any object from Earth is 11.2 km/s. (a) Express this speed in m/s and km/h. Speed, m/s: Speed, km/h: (b) At what temperature would oxygen molecules (molecular mass is equal to 32 g/mol) have an average velocity, vms, equal to Earth's escape velocity 11.2 km/s?Thank u A tank of compressed air of volume 1.00 m^3 is pressurized to 20.8 atm at T= 273 K. A valve is opened, and air is released until the pressure in the tank is 15.3 atm. How many molecules were released? Boltzmann constant is 1.38 × 10-23 J/k.In an experiment, the temperature of a hot gas stream is to be measured by athermocouple with a spherical junction. Due to the nature of this experiment, theresponse time of the thermocouple to register 99 percent of the initial temperaturedifference must be within 5 s. The properties of the thermocouple junction are k =34 W/m·K, ρ= 8400 kg/m3 and Cp =310 J/kg·K. If the heat transfer coefficientbetween the thermocouple junction and the gas is 230 W/m2·K, determine thediameter of the junction. Answer: 0.59 mm