an ideal gas at a pressure of 1 atm and temperature of 27 degree celcius  is compressed adiabatically until its pressure becomes 8 times the intial pressure. Then, the final temperature is?

 

Asked by imtiyazmulla68 | 10th Jan, 2018, 08:24: PM

Expert Answer:

For space adiabatic space process space
space space PV to the power of straight gamma space equals space constant

space space Ideal space gas space equation

space fraction numerator space space PV over denominator straight T end fraction space equals space constant

space space Initial space state
space space space straight P subscript 1 equals 1 space atm comma space space space space space straight T subscript 1 equals 27 space to the power of 0 straight C space equals space 300 space straight K space space space space space space space space space
space space space
space Final space state
space space straight P subscript 2 space equals space 8 space atm comma space space space space space straight T 2 space equals ? space

space straight P subscript 1 space straight x space straight V subscript 1 to the power of straight gamma space equals space straight P subscript 2 space straight x space straight V subscript 2 to the power of straight gamma

space open parentheses fraction numerator space straight V subscript 1 over denominator space straight V subscript 2 end fraction close parentheses to the power of straight gamma space equals open parentheses straight P subscript 2 over straight P subscript 1 space close parentheses space equals space 8

space space straight gamma space for space ideal space gas space 1.66 space

straight V subscript 1 over straight V subscript 2 space equals space 8 to the power of left parenthesis 1 divided by 1.66 right parenthesis space end exponent equals space 3.5 space space

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

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

space space space space space space space space equals fraction numerator 8 over denominator 3.5 end fraction space cross times space 300 space

straight T subscript 2 space space space equals space 686 space straight K

Answered by Varsha | 12th Jan, 2018, 11:20: AM