One-mole-of-steam-is-condensed-at-100-C-the-water-is-cooled-to-0-C-and-frozen-to-ice-Which-of-the-following-statements-are-correct-given-heat-of-vapourization-and-fusion-are-540-cal-gm-and-80-cal-

Question Number 23864 by Tinkutara last updated on 08/Nov/17

One mole of steam is condensed at

100 ° C, the water is cooled to 0 ° C and

frozen to ice . Which of the following

statements are correct, given heat of

vapourization and fusion are 540 cal /

gm and 80 cal / gm ? (average heat

capacity of liquid water = 1 cal {gm}^{- 1}

{degree}^{- 1})

(1) Entropy change during the

condensation of steam is - 26.06 cal / ° C

(2) Entropy change during cooling of

water from 100 ° C to 0 ° C is - 5.62 cal / ° C

(3) Entropy change during freezing of

water at 0 ° C is - 5.27 cal / ° C

(4) Total entropy change is - 36.95

cal / ° C

Answered by ajfour last updated on 09/Nov/17

A l l c o r r e c t (I b e l i e v e) .

\int d S = \int \frac{d Q}{T} .

d u r i n g c o n e n s a t i o n

T = 373 K (c o n s t a n t)

\int d Q = - {m L}_{v a p}

S o △ S_{c o n d e n s a t i o n} = - \frac{18 \times 540}{373} \frac{J}{K}

= - 26.06 J / K

△ S_{c o o l i n g} = \int_{373}^{273} \frac{m c d T}{T}

= - 18 \ln (\frac{373}{273}) \approx - 18 \ln (\frac{124.3}{91})

\approx - 18 \times 2.303 \times (3 \log 5 - 2 \log 3 - 1)

\approx - 18 \times 2.3 \times [3 (1 - 0.3010) - 2 \times 0.4771 - 1]

\approx - 18 \times 2.3 [2.1 - 1.9542]

\approx - 18 \times 2.3 \times 0.145

\approx - 9 \times 2.3 \times 0.29 = 20.7 \times 0.29 J / K

\approx - 6 J / K .

△ S_{f r e e z i n g} = - \frac{{m L}_{f u s i o n}}{T_{f}}

= \frac{- 18 \times 80}{273} = - 5.27 J / K

△ S_{n e t} = - (26 + 6 + 5.3) J / K

= - 37.3 J / K .

Commented by Tinkutara last updated on 09/Nov/17

W h y i n c a l c u l a t i n g Δ S_{c o n d e n s a t i o n} a n d

Δ S_{f r e e z i n g} y o u h a v e t a k e n t h e m t o b e

- m L ? W h y n o t + m L ? I k n o w t h a t

e n t r o p y d e c r e a s e s b u t i n f o r m u l a

t h e r e i s o n l y + s i g n .

Commented by Tinkutara last updated on 10/Nov/17

Thank you very much Sir!

Commented by ajfour last updated on 09/Nov/17

d Q i s h e a t r e c e i v e d b y s y s t e m;

a n d d u r i n g f r e e z i n g o r d u r i n g

c o n d e n s a t i o n h e a t i s g i v e n o u t

b y t h e s y s t e m s o \int d Q = - ∣ m L ∣ .

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