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  3. Chemistry
  4. A gas expands isothermally against a constant external pressure of 1 atm from a volume of 10 dm 3 to a volume of 20 dm 3. It absorbs 300 J of thermal energy from its surroundings. The Δ U is

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Q. A gas expands isothermally against a constant external pressure of $1 \,atm$ from a volume of $10\, dm ^{3}$ to a volume of $20\, dm ^{3}$. It absorbs $300\, J$ of thermal energy from its surroundings. The $\Delta\, U$ is

Bihar CECEBihar CECE 2007Thermodynamics

Solution:

$W=-\int\limits_{V_{1}}^{V_{2}} P d V=-P\left(V_{2}-V_{1}\right)$
$W=-1(20-10)=-10\, d m^{3} \,atm$
$=-10 d m^{3} \times \frac{8.314 \,J K^{-1} \,m o l^{-1}}{0.0821 \,d m^{3} \,K^{-1}\, m o l^{-1}}$
$=-1013\, J$
From 1st law of thermodynamic
$\Delta U=q+W$
$=800 \,J+(-1013\, J)=-213\, J$