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Asked by manvirsingh2242 | 21 Jun, 2022, 04:35: PM

Expert Answer

Let us consider that entropy S is a function of volume V and temperature T

Then we have ,

begin mathsize 14px style d S space equals space open parentheses fraction numerator partial differential S over denominator partial differential T end fraction close parentheses subscript V d T plus space space open parentheses fraction numerator partial differential S over denominator partial differential V end fraction close parentheses subscript T d V end style

.......................(1)

During vapouraisation of water to steam, temperature is constant ,

i.e, dT=0 ......................(2)

By Maxwell's thermodynamics relation, we have

begin mathsize 14px style open parentheses fraction numerator partial differential S over denominator partial differential V end fraction close parentheses subscript T space equals space open parentheses fraction numerator partial differential P over denominator partial differential T end fraction close parentheses subscript V end style

.......................(3)

Using eqn.(2) and eqn.(3) , we rewrite eqn.(1) as

begin mathsize 14px style d S space equals space space open parentheses fraction numerator partial differential P over denominator partial differential T end fraction close parentheses subscript V d V end style

begin mathsize 14px style d Q space equals space T d S space equals space T space open parentheses fraction numerator partial differential P over denominator partial differential T end fraction close parentheses subscript V d V end style

......................(4)

where dQ = m × L is heat absorbed during vapouraisation process, m is mass of water

and L is Latent heat of vapouraisation .

Hence eqn.(4) becomes ,

begin mathsize 14px style m space cross times space L space equals space T space open parentheses fraction numerator partial differential P over denominator partial differential T end fraction close parentheses subscript V d V end style

begin mathsize 14px style L space equals space fraction numerator T space cross times open parentheses begin display style fraction numerator partial differential P over denominator partial differential T end fraction end style close parentheses cross times d V over denominator m end fraction space equals space fraction numerator 373 cross times left parenthesis 13.534 cross times 10 cubed cross times 9.8 cross times 2.7 cross times 10 to the power of negative 2 end exponent space right parenthesis cross times 1673 space cross times space 10 to the power of negative 6 end exponent over denominator 10 to the power of negative 3 end exponent end fraction space J divided by k g end style

( bracketed term in numerator of above expression is ∂P = ρ g h , where ρ is density of mercury ,

g is acceleration due to gravity and h is height given for the measure of pressure )

From above expression, we get latent heat of vapouraistation of water L = 2.235 × 10⁶ J/kg

Answered by Thiyagarajan K | 21 Jun, 2022, 08:09: PM

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