(c) A meteorite made of iron with mass Mmet = 100kg and initial temperature Tmet = 3000k, falls into a large lake with temperature Tlake = 300k. Estimate the total entropy change as the meteorite temperature reaches the lake temperature (In (10) = 2.3) Take * The change of entropy of the meteorite is AS met = Tmet Mmet Ciron dT T

Write down the thermodynamic equations of state for the pressure and entropy which follow from the Helmholtz free energy F. Hence express the heat capacity at constant volume in terms of F. [You may use the definition: dF = −SdT – PdV.]

The entropy S of a system of N spins, which may align either in the upward or in the downward direction, is given by S=-k,N|pln p+(1– p) In(1– p)] . Here k, is the Boltzmann constant. The probabinty of alignment in the upward direction is p. The value of p, at which the entropy is maximum, is (Give your answer upto one decimal place)

Using molecular and system partition functions it is possible to derive the Sackur-Tetrode equation, which allows the computation of absolute entropy from molecular parameters: 2лmkвT S = {NkB + NkB In In [ (2TmkyT) 3/² V h² N In this equation, the quantity V/N is sometimes written as 1/p. = (a) Use this expression to compute the entropy due to translation for one mole of CO₂ gas at 400 K, for which mco2 = 44.01 Daltons, and its molar volume (pressure = 1 bar) is V 0.03326 m³. (Note: 1 Dalton = 1.66053 × 10-27 kg). Be careful with the computation- keep track of units and make sure that the argument of the LN function is unitless. Your answer should be between 100 and 200 J/K if you do everything correctly. (b) If the mass of neon were twice as large (88 instead of 44 Daltons), by how much would the extra mass affect its translational entropy? Report the ratio of the entropy with the heavier mass to that found in part (a).

A plastic bag containing 0.2 kg of water at 20°C is dropped from a height of 0.5 m onto an insulating carpet. Assume that the bag does NOT break. What is the approximate probability that a similar bag sitting on a carpet will do the reverse; that is, spontaneously jump 0.5 m in the air? Express your answer in the form "Probability = 10-x," where x is a number you will calculate. (Hint: Note that ey = 10y÷ln(10).)

Number 3 please

Answer in 90 minutes please.

For a dilute gas of N monatomic particles with mass m and total energy E, use the Sackur- Tetrode equation for the entropy S V = log + NkB to derive expressions for the pressure and internal energy in terms of the temperature T and volume V. [You may use that X₁ = 3πh² N/(mE).] th

Polymers, like rubber, are made of very long molecules, usually tangled up in a configuration that has lots of entropy. As a very crude model of a rubber band, consider a chain of N links, each of length L Imagine that each link has only two possible states, pointing either left or right. The total length L of the rubber band is the net displacement from the beginning of the first link to the end of the last link. Using the thermodynamic identity, you can now express the tension force F in terms of a partial derivative of the entropy. From this expression, compute the tension in terms of L, T , N, and l.

Suppose that 10 distinguishable particles are equipartitioned in a container that has 100 equal-sized compartments. What is the entropy on this system?