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The entropy change associated with the conversion of 1kg of ice at 273 K to water vapours at 383 K is:

( Specific heat of water liquid and water vapour are $4.2kJK^{-1}kg^{-1} and \: 2.0kJ K^{-1}kg^{-1}$ ; heat of liquid fusion and vapourisation of water are $334kJkg^{-1}\: and\: \: 2491kJkg^{-1}$ , respectively ). ( log 273 = 2.436 , log 373=2.572 , log 383 = 2.583)
Option 1)
$2.64kJkg^{-1}K^{-1}$

$\: \:$

Option 2)
$7.90kJkg^{-1}K^{-1}$
Option 3)
$8.49 kJ kg^{-1}K^{-1}$
Option 4)
$9.26\: \: kJkg^{-1}K^{-1}$

Answers (1)

A admin

Entropy for phase transition at constant pressure -

$\Delta S= \frac{\Delta H_{Transition}}{T}$

- wherein

Transition $\Rightarrow$ Fusion, Vaporisition, Sublimation

$\Delta H\Rightarrow$ Enthalpy

$\Delta E\Rightarrow$ Internal Energy

$T\Rightarrow$ Transitional temperature

Entropy for solid and liquid -

$\Delta S= nC\, \ln \frac{T_{f}}{T_{i}}$

or

$\Delta S= ms\, \ln \frac{T_{f}}{T_{i}}$

- wherein

$n=$ no. of moles

$C=$ molar heat capacity

$m=$ mass

$s=$ specific heat capacity

Phase change path

$H_{2}O(S)\underset{\Delta S_{1}}{\rightarrow}H_{2}O(l)\overset{\Delta S_{2}}{\rightarrow}H_{2}O(l)\overset{\Delta S_{3}}{\rightarrow}H_{2}O(g)\overset{\Delta S_{4}}{\rightarrow}H_{2}O(g)$

273 K 273 K 373 K 373 K 383 K

$\Delta S_{1}=\frac{\Delta H_{fusion}}{273}=\frac{334}{273}=1.22$ $\Delta S_{2}=4.2 ln (\frac{373}{273})=1.31$

$\Delta S_{3}=\frac{\Delta H_{vap}}{373}=\frac{2491}{373}=6.67$ $\Delta S_{4}=2.0 ln (\frac{383}{373})=0.05$

$\Delta S \: Total = \Delta S_{1}+\Delta S_{2}+\Delta S_{3}+\Delta S_{4}= 9.26 KJ \: Kg^{-1}K^{-1}$

Option 1)

$2.64kJkg^{-1}K^{-1}$

$\: \:$

Option 2)

$7.90kJkg^{-1}K^{-1}$

Option 3)

$8.49 kJ kg^{-1}K^{-1}$

Option 4)
$9.26\: \: kJkg^{-1}K^{-1}$

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