Fixed mass of an ideal gas contained in a $24.63$ L sealed rigid vessel at 1 atm is heated from $-73^{\circ} \mathrm{C}$ to $27^{\circ} \mathrm{C}$. Calculate change in gibb's energy if entropy of gas is a function of temperature as $\mathrm{S}=2+10^{-2} \mathrm{~T}(\mathrm{~J} / \mathrm{K}):($…

Question

Fixed mass of an ideal gas contained in a $24.63$ L sealed rigid vessel at 1 atm is heated from $-73^{\circ} \mathrm{C}$ to $27^{\circ} \mathrm{C}$. Calculate change in gibb's energy if entropy of gas is a function of temperature as $\mathrm{S}=2+10^{-2} \mathrm{~T}(\mathrm{~J} / \mathrm{K}):($ Use $1 \operatorname{atm} \mathrm{L}=0.1 \mathrm{~kJ})$

Aicharya · Accepted Answer

At constant volume, $\frac{\mathrm{P}_{1}}{\mathrm{~T}_{1}}=\frac{\mathrm{P}_{2}}{\mathrm{~T}_{2}}$
$\Rightarrow \mathrm{P}_{2}=1 \times \frac{300}{200}=\frac{3}{2}$
and $\mathrm{V}_{1}=24.63 \mathrm{~L}$
for single phase
$\because \quad \mathrm{dG}=\mathrm{Vdp}-\mathrm{SdT}$
$\Delta \mathrm{G}=\mathrm{V} \Delta \mathrm{P}-\int\left(2+10^{-2} \mathrm{~T}ight) \mathrm{dT}$
$=1231.5-200-\left(\frac{10^{-2} \times 50,000}{2}ight)$
$=781.5 \mathrm{~J}$

Fixed mass of an ideal gas contained in a $24.63$ L sealed rigid vessel at 1 atm is heated from $-73^{\circ}…

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