Question

The entropy change associated with the conversion of $1\, kg$ of ice at $273\, K$ to water vapours at $383\, K$ is :
(Specific heat of water liquid and water vapour are $4.2 \; kJ \; K^{-1} \; kg^{-1}$ and $2.0 \; kJ \; K^{-1} kg^{-1} $; heat of liquid fusion and vapourisation of water are $344 \; kJ \; kg^{-1}$ and $2491 \; kJ \; kg^{-1}$, respectively).
$(log 273 = 2.436, log 373 = 2.572, log 383 = 2.583)$

• A. $7.90 \; kJ \; kg^{-1} \; K^{-1}$
• B. $2.64 \; kJ \; kg^{-1} \; K^{-1}$
• C. $8.49 \; kJ \; kg^{-1} \; K^{-1}$
• D. $9.26 \; kJ \; kg^{-1} \; K^{-1}$

Answer 1

Answer: (D)

$\underset{273 K }{ H _2 O ( s )} \xrightarrow[\Delta S_1]{} \underset{273\,K}{ H _2 O (\ell) } \xrightarrow[\Delta S_2]{}\underset{373\,K}{ H _2 O (\ell) } \xrightarrow[\Delta S_3]{}\underset{373\,K}{ H _2 O ( g )} \xrightarrow[\Delta S_4]{} \underset{383\,K}{ H _2 O ( g )}$
$\Delta S_1=\frac{\Delta H_{\text {fusion }}}{273}=\frac{334}{273}=1.22$
$\Delta S_2=4.2 \ell N\left(\frac{363}{273}\right)=1.31$
$\Delta S_3=\frac{\Delta H_{\text {vap }}}{373}=\frac{2491}{373}=6.67$
$\Delta S_4=2.0 \ell n\left(\frac{383}{373}\right)=0.05$
$\Delta S_{t o t a l}=9.26 kJ kg ^1 K ^{-1}$