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A gas expands slowly against a variable pressure given by $p = \frac{10}{V}$ bar, where V is volume of gas at each stage of expansion. During expansion from volume 10 L to 100 L the gas undergoes an increase in internal energy of 400 J. How much heat is absorbed by gas during expansion?

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2700 J

1900 J

423 J

2300 J

answer is C.

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Detailed Solution

$\begin{array}{l} W = \int_{10}^{100} \frac{10}{V} d V \\ W = (- 10 \times 2.303 \log \frac{100}{10}) atm - lit \\ W = - 23.03 \times 100 = - 2303 J \\ 400 = - 2303 + q \\ q \approx 2700 \end{array}$

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