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Calculate the increase in entropy of 1 kg of ice when it is converted into steam. Given the specific heat of water is 1 kcal kg oC, latent heat of ice is 80 kcal/kg and the latent heat of steam is 540 k cal/kg.

Asked by ashainy91829 | 06 Nov, 2023, 01:08: PM

Expert Answer

Latent heat of melting of ice , L_f = 80 kcal/kg = 80 × 4.184 kJ/ kg = 335 kJ/kg

Let m = 1 kg be the mass of ice

Change in entropy ΔS₁ for melting of ice at temperature 273 K is

begin mathsize 14px style increment S subscript 1 space equals space fraction numerator increment Q over denominator T end fraction space equals space fraction numerator m space cross times space L subscript f over denominator T end fraction space equals space fraction numerator 1 cross times 375 space over denominator 273 end fraction space k J space equals space 1.374 space space k J space divided by space K end style

Specific heat of water, C_p = 1 kCal = 4.184 kJ/kg

Change in entropy ΔS₂ for increasing the water temperature from 0^o C ( 273 K ) to 100^oC ( 373 K ) is

begin mathsize 14px style increment S subscript 2 space equals space integral subscript 273 superscript 373 fraction numerator increment Q over denominator T end fraction space equals space space m space C subscript p space integral subscript 273 superscript 373 fraction numerator d T over denominator T end fraction end style

begin mathsize 14px style increment S subscript 2 space equals space m space C subscript p space ln left parenthesis 373 divided by 273 right parenthesis space equals space 1 space cross times space 4.184 space cross times space ln left parenthesis 373 divided by 273 right parenthesis space space k J divided by K end style

begin mathsize 14px style increment S subscript 2 space equals space 1.306 space space k J divided by K end style

Latent heat of vapouraisation of water , L_v = 540 kCal / kg = 540 × 4.184 kJ / kg = 2259 kJ/kg

Change in entropy ΔS₃ for converting water at boiling point to steam is

begin mathsize 14px style increment S subscript 3 space equals space fraction numerator m space cross times space L subscript v over denominator T end fraction space equals space fraction numerator 1 cross times 2259 over denominator 373 end fraction space k J divided by k g space equals space 6.056 space space k J divided by k g end style

Total entropy ΔS is

begin mathsize 14px style increment S space equals space increment S subscript 1 space plus space increment S subscript 2 space plus space increment S subscript 3 end style

begin mathsize 14px style increment S space equals space 8.736 space space k J space divided by space k g end style

Answered by Thiyagarajan K | 06 Nov, 2023, 05:31: PM

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