1. Starting with the partition function of a monoatomic...

1. Starting with the partition function of a monoatomic ideal gas with N particles, (a) Find the entropy S as a function V, T(or ?) and N. (Check whether the result is consistent with Sackur-Tetrode equation). (b) Find the chemical potential ? as a function V, T(or ?) and N.

Transcript

00:01 In this question we are talking about partition function so partition function monoatomic here we talk about monoatomic ideal guess monoatomic guess of the n particle so here we talk about n particle monoatomic ideal guess of the n particles now in the first part of this question we need to find the entropy s here we talk about entropy s so let's solve this question entropy s is the function of v t and n so let's find out the function and we're using here in this question we're using the function here in this question we're using the equation of secret secret tetrode equation so this equation where we are we will here using in this problem so let's write the first so we know that the monoatomic ideal guess so in the monoatomic ideal guess let's find the partition function so here you can write the pi n of v t which is equal we can write 1 divided by n factorial multiply we can write v divided by we can write h cube multiply we can write 2 pi m k t so 2 pi m k t raised to we can write 3 divided by 2 raised to we can write value of n this is our equation number one now here we can write the value of a capital a which is equal we can write minus r t here we can multiply ln of here phi or we can say theta n v t now we just substitute value into this formula right phi n not theta now we just simplify we substitute value this value into this formula so let's solve this question we substitute the here phi of n value into this a formula so we can write a which is equal to minus r divided by t ln of multiply we can write 1 divided by n factorial multiply we can write v divided by h cube multiply we can write 2 pi m k t raised to 3 divided by 2 and raised to we can write capital n so this is the value now here a which is equal we can write the final equation is here a multiplied by t ln of here we can write n factorial we just invert it again invert so here you can write h cube divided by v and here we can write 2 pi m k t raised to we can write minus 3 divided by 2 and here we can write raised to here total here whole raised to we can write n so here we can write value is n now we just…

Question

1. Starting with the partition function of a monoatomic ideal gas with N particles, (a) Find the entropy S as a function V, T(or ?) and N. (Check whether the result is consistent with Sackur-Tetrode equation). (b) Find the chemical potential ? as a function V, T(or ?) and N.

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