Physics
Heat
Easy

Question

In an adiabatic process R equals 2 over 3 C subscript v. The pressure of the gas Will be proportional to :

  1. T to the power of 5 divided by 3 end exponent
  2. T to the power of 5 divided by 2 end exponent
  3. T to the power of 5 divided by 4 end exponent
  4. T to the power of 5 divided by 6 end exponent

The correct answer is: T to the power of 5 divided by 2 end exponent


    R equals 2 over 3 C subscript V
text  We know,  end text C subscript p minus C subscript V equals R
table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em rowspacing 3 pt end attributes row cell text  or  end text end cell row cell gamma minus 1 equals R over C subscript v text  or  end text R equals C v left parenthesis gamma minus 1 right parenthesis end cell end table
text  Comparing  end text gamma equals 5 over 3
P to the power of 1 minus gamma end exponent T to the power of straight gamma equals text  constant  end text equals straight K
    text  or  end text space of 1em P proportional to T to the power of left parenthesis gamma divided by gamma minus 1 right parenthesis end exponent comma text  Given  end text gamma equals 5 over 3
fraction numerator gamma over denominator left parenthesis gamma minus 1 right parenthesis end fraction equals 5 over 2
text  So,  end text P proportional to T to the power of 5 divided by 2 end exponent

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