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

Question

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).

Answer 1

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

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