a system has five possible macrostates. The number of microstates for each macrostate is given below: Macrostate A - number of microstates=100 / Macrostate B - number of microstates=200 / Macrostate C - number of microstates=400 / Macrostate D - number of microstates= 800 / Macrostate E - number of microstates=1600 a) what is the probability of a microstate? b)what is the entropy of the system in the units of Kb? c) what is the probability of macrostate E? d)what is the most probable macrostate?

a system has five possible macrostates. The number of microstates for each macrostate is given below: Macrostate A - number of microstates=100 / Macrostate B - number of microstates=200 / Macrostate C - number of microstates=400 / Macrostate D - number of microstates= 800 / Macrostate E - number of microstates=1600 a) what is the probability of a microstate? b)what is the entropy of the system in the units of Kb? c) what is the probability of macrostate E? d)what is the most probable macrostate?

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For this problem, we want to estimate the answer, so our assumptions may be a little unrealistic. Suppose we want to estimate how much air we need to send to a space station, assuming we cannot recycle air. Suppose four astronauts are in a spherical space station. If each of them typically breathes about 500 cm³of air with each breathe, and take 15 breathes per minute (average resting value): a. What is the volume of air you would need in the space station if these four astronauts stayed for a full year? b. If the density of air is 1.25 kg/m³ and it costs (thanks to SpaceX) a mere $100/kg to send objects to the space station, how much money would the astronaut air supply cost?
Parts B, C, and D. Statistical mechanics
The question is whether these relationships are linear or non-linear, can you please inform me on how I'd be able to tell?
The Arhennius viscosity model describes how viscosity u depends on temperature 1: u = uo e E/RT 1 DVD DVD Here u is viscosity (Pa.s), I is the temperature (in "Kelvin), E is the activation energy (J mol¹), R is the universal gas constant (R = 8.3145 J mol¹¹ K¹) and U is a constant (Pa s). Ensure all your numerical answers are provided, accurate to 4 significant figures. Linearise this non-linear equation to allow the least squares fitting, i.e. write it in the form y = a + a₁x. Identify the independent (x) and dependent (y) variables and write the linearised equation in the answer boxes, clearly defining what ao and a₁ are equal to in terms of up, E and R. y: ao: a₁: X: IOHO OHO Man