Answer
397.2k+ views
Hint: Entropy can be defined as the disorder in a system. When a substance changes its state, its entropy also changes. The gases have highest entropy while the solids possess lowest entropy. The entropy change in a system can be calculated from the two formulas given as-
$\Delta S$= $\dfrac{{\Delta {H_{Transition}}}}{T}$
$\Delta S$= $ms\ln \dfrac{{{T_f}}}{{{T_i}}}$
Where $\Delta S$ is the entropy change
‘n’ is the number of moles
C is the molar heat capacity
${T_f}$is final temperature
${T_i}$is initial temperature
‘m’ is the mass
‘s’ is the specific heat capacity.
Complete step by step answer :
Let us start by writing what is given to us and what we need to find.
Thus, Given :
Mass of ice = 1 kg
Initial temperature = 273 K
Final temperature = 383 K
Further, we have been given that Specific heat of water liquid = 4.2 $kJ{K^{ - 1}}k{g^{ - 1}}$
Specific heat of water vapour = 2.0$kJ{K^{ - 1}}k{g^{ - 1}}$
Latent heat of fusion of water = 344$kJk{g^{ - 1}}$
Latent heat of vaporisation of water = 2491$kJk{g^{ - 1}}$
To find :
Entropy change
We have the formula for entropy change is as -
$\Delta S$= $\dfrac{{\Delta {H_{Transition}}}}{T}$
$\Delta S$= $nC\ln \dfrac{{{T_f}}}{{{T_i}}}$
$\Delta S$= $ms\ln \dfrac{{{T_f}}}{{{T_i}}}$
Where $\Delta S$ is the entropy change
‘n’ is the number of moles
C is the molar heat capacity
${T_f}$is final temperature
${T_i}$is initial temperature
‘m’ is the mass
‘s’ is the specific heat capacity.
We are converting the solid ice into water vapour which is a gas. The phase change for this can be as -
${H_2}O(s)\xrightarrow{{\Delta {S_1}}}{H_2}O(l)\xrightarrow{{\Delta {S_2}}}{H_2}O(l)\xrightarrow{{\Delta {S_3}}}{H_2}O(g)\xrightarrow{{\Delta {S_4}}}{H_2}O(g)$
$\Delta {S_1}$= $\dfrac{{\Delta {H_{FUSION}}}}{T}$
$\Delta {S_1}$= $\dfrac{{334}}{{273}}$
$\Delta {S_1}$= 1.22
$\Delta {S_2}$= $ms\ln \dfrac{{{T_f}}}{{{T_i}}}$
$\Delta {S_2}$= $4.2\ln \dfrac{{383}}{{273}}$
$\Delta {S_2}$= 1.31
$\Delta {S_3}$= $\dfrac{{\Delta {H_{vaporisation}}}}{T}$
$\Delta {S_3}$= $\dfrac{{2491}}{{373}}$
$\Delta {S_3}$= 6.67
$\Delta {S_4}$= $ms\ln \dfrac{{{T_f}}}{{{T_i}}}$
$\Delta {S_4}$= $2.0\ln \dfrac{{383}}{{273}}$
$\Delta {S_4}$= 0.05
$\Delta {S_{TOTAL}}$=$\Delta {S_1}$+$\Delta {S_2}$+$\Delta {S_3}$+$\Delta {S_4}$
$\Delta {S_{TOTAL}}$= 1.22 + 1.31 + 6.67 + 0.05
$\Delta {S_{TOTAL}}$= 9.25 $kJ{K^{ - 1}}k{g^{ - 1}}$
This value is similar to in option d.).
So, the correct answer is option d.).
Note: The gases have least intermolecular forces. So, the molecules are not bonded to each other and thus are in random motion. So, the gases have highest entropy while solids have lowest entropy. When we are observing the phase transitions, firstly, the solid will convert to liquid and then there will be a rise in temperature of liquid by heating and when the sufficient temperature has reached then it will convert into gas. After this, there will be a temperature increase in gas.
$\Delta S$= $\dfrac{{\Delta {H_{Transition}}}}{T}$
$\Delta S$= $ms\ln \dfrac{{{T_f}}}{{{T_i}}}$
Where $\Delta S$ is the entropy change
‘n’ is the number of moles
C is the molar heat capacity
${T_f}$is final temperature
${T_i}$is initial temperature
‘m’ is the mass
‘s’ is the specific heat capacity.
Complete step by step answer :
Let us start by writing what is given to us and what we need to find.
Thus, Given :
Mass of ice = 1 kg
Initial temperature = 273 K
Final temperature = 383 K
Further, we have been given that Specific heat of water liquid = 4.2 $kJ{K^{ - 1}}k{g^{ - 1}}$
Specific heat of water vapour = 2.0$kJ{K^{ - 1}}k{g^{ - 1}}$
Latent heat of fusion of water = 344$kJk{g^{ - 1}}$
Latent heat of vaporisation of water = 2491$kJk{g^{ - 1}}$
To find :
Entropy change
We have the formula for entropy change is as -
$\Delta S$= $\dfrac{{\Delta {H_{Transition}}}}{T}$
$\Delta S$= $nC\ln \dfrac{{{T_f}}}{{{T_i}}}$
$\Delta S$= $ms\ln \dfrac{{{T_f}}}{{{T_i}}}$
Where $\Delta S$ is the entropy change
‘n’ is the number of moles
C is the molar heat capacity
${T_f}$is final temperature
${T_i}$is initial temperature
‘m’ is the mass
‘s’ is the specific heat capacity.
We are converting the solid ice into water vapour which is a gas. The phase change for this can be as -
${H_2}O(s)\xrightarrow{{\Delta {S_1}}}{H_2}O(l)\xrightarrow{{\Delta {S_2}}}{H_2}O(l)\xrightarrow{{\Delta {S_3}}}{H_2}O(g)\xrightarrow{{\Delta {S_4}}}{H_2}O(g)$
$\Delta {S_1}$= $\dfrac{{\Delta {H_{FUSION}}}}{T}$
$\Delta {S_1}$= $\dfrac{{334}}{{273}}$
$\Delta {S_1}$= 1.22
$\Delta {S_2}$= $ms\ln \dfrac{{{T_f}}}{{{T_i}}}$
$\Delta {S_2}$= $4.2\ln \dfrac{{383}}{{273}}$
$\Delta {S_2}$= 1.31
$\Delta {S_3}$= $\dfrac{{\Delta {H_{vaporisation}}}}{T}$
$\Delta {S_3}$= $\dfrac{{2491}}{{373}}$
$\Delta {S_3}$= 6.67
$\Delta {S_4}$= $ms\ln \dfrac{{{T_f}}}{{{T_i}}}$
$\Delta {S_4}$= $2.0\ln \dfrac{{383}}{{273}}$
$\Delta {S_4}$= 0.05
$\Delta {S_{TOTAL}}$=$\Delta {S_1}$+$\Delta {S_2}$+$\Delta {S_3}$+$\Delta {S_4}$
$\Delta {S_{TOTAL}}$= 1.22 + 1.31 + 6.67 + 0.05
$\Delta {S_{TOTAL}}$= 9.25 $kJ{K^{ - 1}}k{g^{ - 1}}$
This value is similar to in option d.).
So, the correct answer is option d.).
Note: The gases have least intermolecular forces. So, the molecules are not bonded to each other and thus are in random motion. So, the gases have highest entropy while solids have lowest entropy. When we are observing the phase transitions, firstly, the solid will convert to liquid and then there will be a rise in temperature of liquid by heating and when the sufficient temperature has reached then it will convert into gas. After this, there will be a temperature increase in gas.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)