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1st Law of Thermodynamics

5 mol of gas ...

Question

5 mol of gas at 5 atm pressure contained in a 100L cylinder absorbed 30.26 kJ of heat when it expanded to 200L at 2atm pressure. The change in internal energy of gas is:

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Solution

For case $1$
$P V = n R T$
$T = \frac{P V}{n R} = \frac{5 \times 100}{5 \times 0.0821} = 1218 K$
For case $2$
$T = \frac{P V}{n R} = \frac{2 \times 200}{5 \times 0.0821} = 974.42 K$
Now, change in internal energy
$Δ u = q - Δ p Δ v$
$= 30.26 - [(2 - 5) (200 - 100)] / 1000$
$= 30.56 k J$

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