Answer to Question #121473 in Mechanical Engineering for INDRAJIT SOMNATH WADGAVE

Question #121473
Calculate the value of the translational partition function of O2 at 1000 K for a volume of 1 m3. Submit your answer multiplied by 10−32 (i.e. if you calculate 4.2e33, input 42).
Expert's answer

Here we have to find the partition function of oxygen we know that mass of oxygen is = 32

Now we will calculate the de borglies thermal wavelength using formula

Λ="\\frac{h}{\\sqrt {2 \\pi m k_B T}}"

Here, T= 1000 K, h= plancks constant, "k_B=" Boltzmann constant

Λ="\\frac{6.67\\times 10 ^{-34}}{\\sqrt {2 \\times 3.14 \\times 2\\times32\\times 1.67 \\times 10^{-27} \\times 1.38 \\times 10^{-23}\\times 1000}}"

Λ= "6.9 \\times 10 ^{-12}"

And for the partition function we know that

"q_{tr}= \\frac{V}{\u039b^3}= \\frac{1}{(6.9\\times 10 ^{-12})^3} = 30.38 \\times 10 ^{32}" = so here we will input only 30 as per the question

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