Consider a case of n particles and two compartments, if n1 is the number of particles in one compartment and remaining n2=n-n1 particles in other compartment, then the number of microstates in the macrostate (n1, n-n1) or thermodynamic probability is
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A: Entropy change = [Heat change in process÷ Temperature ] Heat change = 30J Temperature = 300K
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- For a system of n distinguishable particles to be distributed in two similar compartments, the total number of microstates for n particles is _____.A box contains 100 atoms in a configuration that has 50 atoms in each half of the box. Suppose that you could count the different microstates associated with this configuration at the rate of 100 billion states per second, using a supercomputer. Without written calculation, guess how much computing time you would need: a day, a year, or much more than a year.22. (2 points) What is the probability that exactly two customers arriving at the drive through lane in a fifteen minutes interval? (a) 0.2249 (b) 0.1378 (c) 0.2375 (d) 0.1237 23. (2 points) What is the probability that less than two customers arrive at the drive through lane in a fifteen minutes interval? (а) 0.2759 (b) 0.1991 (c) 0.1245 (d) 0.1874 24. (2 points) What is the probability that two or more customers arrive at the drive through lane in a fifteen minutes interval? (а) 0.8236 (b) 0.8009 (c) 0.7235 (d) 0.8921
- Suppose you receive an average of 4 phone calls per day. What is the probability that on a given day you receive no phone calls? Just one call? Exactly 4 calls?Problem 5: On a hot day, the freezers in a particular ice cream shop maintain an average temperature of T = -18° C while the temperature of the surroundings is T = 29° C. Randomized Variables T₂ = -18° C Th=29° C Part (a) Calculate the maximum coefficient of performance COP for the freezers. ✓ Correct! COPC=5.400 sin() cos cotan() asin() atan() acotan() cosh() tan() acos() E sinh() tanh() cotanh() Degrees O Radians Part (b) If the work input to the freezer is W = 2.3 kJ and the freezer actually removes Qc = 13.6 × 10³ J from the ice cream each second, what is the real coefficient of performance? COP = 5.910 ✓ Correct! Part (c) An employee puts m = 1.15 kg of melted ice cream at To=4.5° C into the freezer. Assuming that the ice cream freezes at T₁ = -1.0° C, how long in seconds will it take for the ice cream to reach its freezing temperature? Take specific heat capacity of the melted ice cream as c = 4,000.0 J/(kg.K). At₁ = ( 7 8 9 4 5 1 2 3 0 sin() cos( cotan() asin() atan() acotan…Suppose you have a classical system that consists of N particles moving in three dimensions. You calculate the entropy for the system using a phase space cell size ho and get the value So. a) Show that if you calculated the entropy using a cell size h₁ = ho/2, you would get the value S₁ = S₁ + 3Nk In2. b) Find the value you would get if you calculated the entropy using cell size aho, where a is a positive dimensionless constant.
- Assume you are using the attached pressure gauge and a thermocouple with a temperature uncertainty of +/- 1C; assuming ideal gas how accurately can you report the molar volume n/V=RT/P?Problem 1: In statistical mechanics, the internal energy of an ideal gas is given by: N. aNkB 2/3 (3NKB U = U(S,V) = е where a is a constant. 1- Show that the variation of the internal energy is given by: 2 dS - \3V 2 dU = dV \3NkB 2- Using the fundamental relation of thermodynamic dU = T.ds – p. dV, show that the equation of state PV = nRT follows from the first expression of U.dU =T dS – P dV Re-arrange the thermodynamic identity by solving for dS. Assume we are applying this new expression to an ideal gas, re-write the du term in terms of the appropriate heat capacity and temperature. Re-write the coefficient of the dV term in terms of volume. Connect these “classical" expressions for entropy to the "modern" interpretation where we are concerned with the uncertainty associated with position and momentum of the particles in an ideal gas. Answer with sentences. Now, re-write the expression in terms of enthalpy so you can connect entropy with enthalpy. Expalin why this final expression makes sense.
- Entropy (s) is aun extensive variable . & S(U,V,N) Uo Internal Energy V→ Volume Number of particles find an Euler equation For entropevii) Consider a case of a particles and two compartments, if m is the number of particles in one compartment and remaining n=-) particles in other compartment, then the mumber of microstates in the macrostate (n. -m) or thermodynamie probability is a) W(4.a- 4) = b) H(2, n-n)=. (s -, 4' (1 + 1, )!A company wants to evaluate its attrition rate, in other words, how long new hires stay with the company. Over the years, they have established the following probability distribution. Let X = the number of years a new hire will stay with the company. Let P(x) = the probability that a new hire will stay with the company x years.On average, how long would you expect a new hire to stay with the company? ____________