Answer
418.2k+ views
Hint: In thermodynamics, there is no work in a system, and work is an operation performed by or on a system. Gases can work against continuous exterior pressure by expansion or compression. Gas work is often also called pressure-volume or $\,PV\,$ work.
Formula used:
$PV = nRT\,$
Where, $\,P = \,$Pressure
$\,V = \,$Volume
$\,n = \,$number of moles
$\,R = \,$Universal gas constant
$\,T = \,$absolute temperature
$\,W = - {P_{ext}} \times \Delta V$
Where $\,W = \,$Work
$\,{P_{ext}} = \,$External Pressure
$\,\Delta V = \,$Change in volume
Complete step by step solution:
Let us first calculate volume of water before vaporization;
$V = \dfrac{m}{d}\,$
Where, $\,V = \,$volume, $\,m = \,$mass and $\,d = \,$density
Here, we have one mole of water which is equal to $\,18g\,$
Therefore, $\,V = \dfrac{{18g}}{{1g/ml}}\,$
As the density of one mole of water is equal to $\,1g/ml\,$at $\,373K\,$
Therefore by solving the equation we get, $\,{V_1} = 18ml\, = 0.018l\,$
Now, let’s calculate $\,{V_2}\,$ which is the volume of water after vaporization;
$P{V_2} = nRT\,$
Where, $\,P = \,$ Pressure
$\,{V_2} = \,$ Volume after vaporization
$\,n = \,$ number of moles
$\,R = \,$ Universal gas constant
$\,T = \,$ absolute temperature
From this we get;
$\,{V_2} = \dfrac{{nRT}}{P}\,$ as per ideal gas equation mentioned above
$\,n = 1,\,R = 0.0821L.atm/mol.K,\,T = 373K,P = 1atm\,$
Substituting them in the equation we get;
$\, \Rightarrow \dfrac{{1 \times 0.0821 \times 373}}{1} = 30.6l\,$
Here $\,{V_1}\,$ is negligible with respect to $\,{V_2}\,$, So we can ignore $\,{V_1}\,$and therefore, $\,\Delta V = 30.6l\,$
Now, let us calculate the work done here,
$W = - {P_{ext}} \times \Delta V\,$
Where $\,W = \,$Work
$\,{P_{ext}} = \,$External Pressure
$\,\Delta V = \,$Change in volume
Here, by converting the unit of volume and pressure we get;
$\,\Delta V = 30.6l = 30.6 \times {10^{ - 3}}{m^3}\,$and $\,P = 1atm = 101325Pascal\,$
Therefore, $\,W = \, - 101325 \times 30.6 \times {10^{ - 3}}\,$
$\, = - 3100J\,$
Here, a negative sign shows that work is done by the system.
So, for this question option A is the correct answer.
Note:
Work done by a system in thermodynamics is the energy transmitted by the system to its surroundings by a process by which the system can exert macroscopic forces on its surroundings naturally, where those forces and their external effects can be calculated. So, in sign conventions, the energy transmitted here is represented as negative work done by the system on its surroundings.
Formula used:
$PV = nRT\,$
Where, $\,P = \,$Pressure
$\,V = \,$Volume
$\,n = \,$number of moles
$\,R = \,$Universal gas constant
$\,T = \,$absolute temperature
$\,W = - {P_{ext}} \times \Delta V$
Where $\,W = \,$Work
$\,{P_{ext}} = \,$External Pressure
$\,\Delta V = \,$Change in volume
Complete step by step solution:
Let us first calculate volume of water before vaporization;
$V = \dfrac{m}{d}\,$
Where, $\,V = \,$volume, $\,m = \,$mass and $\,d = \,$density
Here, we have one mole of water which is equal to $\,18g\,$
Therefore, $\,V = \dfrac{{18g}}{{1g/ml}}\,$
As the density of one mole of water is equal to $\,1g/ml\,$at $\,373K\,$
Therefore by solving the equation we get, $\,{V_1} = 18ml\, = 0.018l\,$
Now, let’s calculate $\,{V_2}\,$ which is the volume of water after vaporization;
$P{V_2} = nRT\,$
Where, $\,P = \,$ Pressure
$\,{V_2} = \,$ Volume after vaporization
$\,n = \,$ number of moles
$\,R = \,$ Universal gas constant
$\,T = \,$ absolute temperature
From this we get;
$\,{V_2} = \dfrac{{nRT}}{P}\,$ as per ideal gas equation mentioned above
$\,n = 1,\,R = 0.0821L.atm/mol.K,\,T = 373K,P = 1atm\,$
Substituting them in the equation we get;
$\, \Rightarrow \dfrac{{1 \times 0.0821 \times 373}}{1} = 30.6l\,$
Here $\,{V_1}\,$ is negligible with respect to $\,{V_2}\,$, So we can ignore $\,{V_1}\,$and therefore, $\,\Delta V = 30.6l\,$
Now, let us calculate the work done here,
$W = - {P_{ext}} \times \Delta V\,$
Where $\,W = \,$Work
$\,{P_{ext}} = \,$External Pressure
$\,\Delta V = \,$Change in volume
Here, by converting the unit of volume and pressure we get;
$\,\Delta V = 30.6l = 30.6 \times {10^{ - 3}}{m^3}\,$and $\,P = 1atm = 101325Pascal\,$
Therefore, $\,W = \, - 101325 \times 30.6 \times {10^{ - 3}}\,$
$\, = - 3100J\,$
Here, a negative sign shows that work is done by the system.
So, for this question option A is the correct answer.
Note:
Work done by a system in thermodynamics is the energy transmitted by the system to its surroundings by a process by which the system can exert macroscopic forces on its surroundings naturally, where those forces and their external effects can be calculated. So, in sign conventions, the energy transmitted here is represented as negative work done by the system on its surroundings.
Recently Updated Pages
Mark and label the given geoinformation on the outline class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
When people say No pun intended what does that mea class 8 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Name the states which share their boundary with Indias class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give an account of the Northern Plains of India class 9 social science 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)
Advantages and disadvantages of science
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Bimbisara was the founder of dynasty A Nanda B Haryanka class 6 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)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
10 examples of evaporation in daily life with explanations
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![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)
How do you graph the function fx 4x class 9 maths 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)