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Fixed amount of an ideal gas contained in a sealed rigid vessel(V=24.6l) at 1 bar is heated reversibly from 27degreeC to 127 degree C.Determine change in gibbs energy in joule if entropy of gas S=10+10^-2 (J/k).

Asked by m.nilu 25th September 2018, 1:47 PM
Answered by Expert
Answer:
Given:
 
P1 = 1 atm
 
straight T subscript 1 space equals space minus 73 space to the power of degree straight C

space space space space space space equals space 270 space straight K

straight T subscript 2 space equals space 27 space to the power of degree straight C

space space space space space equals space 300 space straight K

straight V equals space 24.63 space litre

We space have comma

straight P subscript 1 over straight T subscript 1 equals space straight P subscript 2 over straight T subscript 2 space

straight P subscript 2 space equals space fraction numerator straight P subscript 1 straight T subscript 2 space over denominator straight T subscript 1 space end fraction

space space space space space space equals fraction numerator 1 cross times 300 over denominator 200 end fraction

straight P subscript 2 space equals space 1.5 space atm
Differential equation for free energy,
 
dG space equals space Vdp space minus SdT

integral subscript 1 superscript 2 space dG space equals space straight G subscript 2 space minus straight G subscript 1 space equals space increment straight G

increment straight G space equals space straight V space integral subscript 1 superscript 2 space dP space minus space integral subscript 1 superscript 2 space SdT

space space space space space space space equals straight V space open parentheses increment straight P close parentheses minus space integral subscript 200 superscript 300 space open parentheses 2 space plus space 10 to the power of negative 2 end exponent space straight T close parentheses space dT

space space space space space space space space equals space 24.61 space open parentheses 1.5 minus 1 close parentheses space minus space 2 open parentheses 300 minus 200 close parentheses minus space 10 to the power of negative 2 end exponent over 2 open square brackets open parentheses 300 close parentheses squared space minus space open parentheses 200 close parentheses squared close square brackets

space space space space space space space space equals 12.30 space minus space 200 space minus space 10 to the power of negative 2 end exponent over 2 open parentheses 5 cross times 10 to the power of 4 close parentheses

space space space space space space space equals space 12.30 space minus space 200 space minus space fraction numerator 5 cross times 10 squared over denominator 2 end fraction

1 space atm space straight L space equals space 0.1 space kJ

space space space space space space space space space space space equals space 1230 space minus space 200 space minus space fraction numerator 5 cross times 10 squared over denominator 2 end fraction

space space space space space space space space space space space equals space 1230 space minus 450

space space space space increment straight G space equals space 780 space straight J
Change in Gibbs energy is 780 J.

Answered by Expert 15th October 2018, 3:00 PM
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