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- In Figure all possible distributions and microstates are shown for four different particles shared between two boxes. Determine the entropy change, ΔS, if the particles are initially evenly distributed between the two boxes,but upon redistribution all end up in Box (b).According to the Debye equation the heatthe capacity of a solid is proportional to the temperaturecubed at low temperatures, Cp(T) = σT3, where σis a constant. Show that the entropy at a temperatureT0 is given by S(T0) = Cp(T0)/3 when the Debyeequation holds.a box of mass 10.0 kg and intaial velocity 3.0 m/s slides along a floor and comes to a rest due to friction. estimate the total cahnge in entropy of the universe. assume everthing occures at room tempeture of 293 k
- 5RT3 a. A piece of metal of molar heat capacity Cp is heated from 300K to 500K at 2 constant pressure. Calculate the change of entropy, assuming the volume change is negligible.In the Figure below, all possible distributions and microstates are shown for four different particles shared between two boxes. Determine the entropy change, ΔS, if the particles are initially evenly distributed between the two boxes, but upon redistribution, all end up in Box (b).Starting with the Clausius Inequality, ∂S ≥ ∂q/T, can you prove that, under conditions of constant pressure and entropy, for the total entropy to increase, ∂H ≤ 0 J?
- Prove that the entropy of mixing of an ideal mixture has aninfinite slope, when plotted vs. x, at x = 0 and x = l.Suppose that 10 distinguishable particles are equipartitioned in a container that has 100 equal-sized compartments. What is the entropy on this system?Calculate the entropy change for a hundredfold expansion of a mole of ideal gas isothermally.
- given as a systemic partition function. Using this link, calculate pressure, entropy and internal energy (a constant)A piece of material is brought from temperature T; to temperature Tƒby placing it in contact with a series of N reservoirs at temperature T;+AT, T;+2AT, ... ,T;+NAT=T;. Assuming that the heat capacity of the material C, is temperature independent, calculate the entropy change of the total system, material plus reservoirs. What is the entropy change in the limit N → ∞ for fixed T;-T;?(a) A 5.0-kg rock at a temperature of 20 °C is dropped into a shallow lake also at 20 °C from a height of 1.0 × 103 m . What is the resulting change in entropy of the universe? (b) If the temperature of the rock is 100 °C when it is dropped, what is the change of entropy of the universe? Assume that air friction is negligible (not a good assumption) and that c = 860 J/kg · K is the specific heat of the rock.