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A cylinder contains N moles of diatonur gas at Tempeture T. Heat is supplied such that temperature remains constant but n moles gas converted to monoatomic gas. What will be the change in Kinetic Energy.

Option: 1
0

Option: 2
$\frac{5}{2} n R T$

Option: 3
$\frac{1}{2}n R T$

Option: 4
$\frac{3}{2} nR T$

Answers (1)

best_answer

<p><img alt="K_i=\frac{5}{2} R T N \\" src="https://latex.codecogs.com/gif.latex?K_i%3D%5Cfrac%7B5%7D%7B2%7D%20R%20T%20N%20%5C%5C" /></p>

<p><img alt="k_f=\frac{5}{2} R T(N-n)+\frac{3}{2} R T 2 n" src="https://latex.codecogs.com/gif.latex?k_f%3D%5Cfrac%7B5%7D%7B2%7D%20R%20T%28N-n%29&plus;%5Cfrac%7B3%7D%7B2%7D%20R%20T%202%20n" /><br />
<br />
<img alt="\Delta K =K_f-K_i \\" src="https://latex.codecogs.com/gif.latex?%5CDelta%20K%20%3DK_f-K_i%20%5C%5C" /><br />
          <img alt="=\left(\frac{5}{2} R T(N-n)+\frac{3}{2} R T 2 n\right)-\frac{5}{2} R T N \\" src="https://latex.codecogs.com/gif.latex?%3D%5Cleft%28%5Cfrac%7B5%7D%7B2%7D%20R%20T%28N-n%29&plus;%5Cfrac%7B3%7D%7B2%7D%20R%20T%202%20n%5Cright%29-%5Cfrac%7B5%7D%7B2%7D%20R%20T%20N%20%5C%5C" /></p>

<p>           <img alt="=n R T\left(3-\frac{5}{2}\right)=\frac{1}{2} n R T" src="https://latex.codecogs.com/gif.latex?%3Dn%20R%20T%5Cleft%283-%5Cfrac%7B5%7D%7B2%7D%5Cright%29%3D%5Cfrac%7B1%7D%7B2%7D%20n%20R%20T" /><br />
 </p>

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Rakesh

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