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Potential Energy of Two Point Charges

5 moles of ...

Question

5 moles of $N_{2}$ at 5 atm pressure contained in a 100 L cylinder absorbed 30.26 kJ of heat when it expanded to 200 L at 2 atm. What is the change in internal energy of the gas ?

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Solution

$\begin{matrix} Δ U = q + w & P V = n R T q = + 30.26 K J & n R T = 5 \times 100 W = - n R T ℓ n \frac{V_{2}}{V_{1}} & [c o n s i d e r i n g r e v e r s i b l e p r o c e s s] W = - 5 \times 100 ℓ n \frac{200}{100} \Rightarrow - 500 ℓ n 2 \Rightarrow - 500 (0.693) \Rightarrow - 346.5 J Δ U = q + w \Rightarrow 30.26 K J - 346.5 J \Rightarrow 30.26 K J - 0.3465 K J Δ U = 29.9135 K J \end{matrix}$

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