1. Consider heat flow in a semi-infinite plate, where the side edges are maintained at zero temperature, and the bottom edge at Tosin(tx/£). Determine the steady-state temperature in the plate. Hint: The Fourier inversion is trivial here; no integration is required! X
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- In class, we said that if the surface temperature oscillates as T(t, z = 0) = To sinwt, the temperature at a depth z will be (-V Tt, 2) — То еxр z) sin ( wt 2к • Z V 2K The negative sign in the exponential term tells us that the amplitude of the temperature variation decreases with depth. One way to assess how deep we have to get before the temperature variation is "small" is to find where the maximum value reached is To/e, or To exp(-1). This occurs where (Vä:2) = 1. (The angular frequency w = 2nf.) 2к 10-6 m²s-1. For Earth rocks, we can take the thermal diffusivity K = At what depth is the temperature variation “small" (To/e) for (a) a diurnal variation in surface temperature (f = 1/day= 1/86400 s)? (b) a seasonal variation (f = 1/year)? (c) a Milankovitch forcing of 100,000 years (f = 1/100,000 yr)?2.00 mol of helium and 1.00 mol of argon are separated by a very thin barrier. Initially the helium has 7500 J of thermal energy. The helium gains 2500 J of energy as the gases interact and come to thermal equilibrium by exchanging energy via collisions at the boundary. What was the initial temperature of the argon? What is the thermal energy of the argon at the equilibrium temperature? Express your answer with the appropriate units. ► View Available Hint(s) (Eth f) Ar = 5000 J Submit Previous Answers Correct Part C What was the initial temperature of the argon? Express your answer in kelvins.The density of gray and white tin are 5.77×103 kg/m3 and 7.37×103 kg/m3. The latent heat for the transition between gray and white tin is 2.20×103 J/mol. The atomic weight of tin is 118.7. Calculate the slope of the tangent of the coexistence curve of gray and white tin at T=376 K. Select one: a.dP/dT=−14.2 atm/K b.dP/dT=−12.9 atm/K c.dP/dT=−14.6 Pa/K d.dP/dT=−12.3 Pa/K
- During a physics experiment, helium gas is cooled to a temperature of 17.0 K at a pressure of 5.00×10−2 atm. What is the mean free path in the gas? What is the rms speed of the atoms? What is the average energy per atom?In 1995 a research group led by Eric Cornell and Carl Wiemann at the University of Colorado successfully cooled Rubidium atoms to the 20-200 nk temperature range. Assuming (incorrectly) that the Rubidium atoms behave like particles of a classical ideal gas, calculate the RMS speed of a Rubidium atom at a temperature of 36.0 nk. In the experiments one particular isotope of Rubidium was used, Rubidium-87. The molar mass of this isotope is 86.91 g/mol. Submit Answer Tries 0/122.a. What is the total Power emitted (in the form of electromagnetic radiation) by a solid hemisphere of emissivity, e = 1, if its radius is 0.70m, and it is maintained at a temperature of 1280 K ? 2.b. What is the total energy emitted by this object in 90 seconds?
- The density of ice is 917 kg/m3.Use the Clausius-Clapeyron relation to explain why the slope of the phase boundary between water and ice is negative.Can anyone help me with this questionConsider the partition function Z=>e %3D Calculate the specific heat of the system. (a) ke- Bho 1-e-Bha 2. (b) k 1-e Bho (c) ke-Bha 1 1-e-Bho (d) ke Bho 1+e-Bh
- 2 Thermo Physics The ground state of Cyanogen gas (Energy = 0 eV) and 1st excited state is (E = 4.7x10^-4eV) can be separately identified by their spectra. An astronomer determines that on interstellar gas has a ratio of 10:1. 10 molecules of cyanogen gas to every 1 excited state. Use this to determine the temperature of the gas?Imagine a photon gas at an initial temperature of T = 1.4 K. What is the temperature of the photon gas (in K) after it has undergone a reversible adiabatic expansion to 2 times its original volume?Complete the following statement: The absolute temperature of an ideal gas is directly proportional to O the average momentum of a molecule of the gas. O the amount of heat required to raise the temperature of the gas by 1 Cº. O the number of molecules in the sample. O the relative increase in volume of the gas for a temperature increase of 1 Cº. O the average kinetic energy of the gas.