Question

The entropy change associated with the conversion of $1kg$ of ice at $273K$ to water vapours at $383K$ is :
(Specific heat of water liquid and water vapour are $4.2kJ{K}^{-1}k{g}^{-1}$ and $2.0kJ{K}^{-1}k{g}^{-1}$; heat of liquid fusion and vapourisation of water are $344kJk{g}^{-1}$ and $2491kJk{g}^{-1}$, respectively).
$(log273=2.436,log373=2.572,log383=2.583)$

• A. $7.90kJk{g}^{-1}{K}^{-1}$
• B. $2.64kJk{g}^{-1}{K}^{-1}$
• C. $8.49kJk{g}^{-1}{K}^{-1}$
• D. $9.26kJk{g}^{-1}{K}^{-1}$

Answer 1

Answer: (D)

$\underset{273K}{H_{2}O(s)}\underset{\Delta S_1}{\to }\underset{273K}{H_{2}O(\ell )}\underset{\Delta S_2}{\to }\underset{373K}{H_{2}O(\ell )}\underset{\Delta S_3}{\to }\underset{373K}{H_{2}O(g)}\underset{\Delta S_4}{\to }\underset{383K}{H_{2}O(g)}$
$\Delta S_1=\frac{\Delta H_{\text{fusion }}}{273}=\frac{334}{273}=1.22$
$\Delta S_2=4.2\ell N\left(\frac{363}{273}\right)=1.31$
$\Delta S_3=\frac{\Delta H_{\text{vap }}}{373}=\frac{2491}{373}=6.67$
$\Delta S_4=2.0\ell n\left(\frac{383}{373}\right)=0.05$
$\Delta S_{total}=9.26kJk{g}^1{K}^{-1}$