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Mechanical Properties Of Fluids

Question
CBSEENPH11020319

A thermally insulated vessel contains an ideal gas of molecular mass M and ratio of specific heat γ.It is moving with speed v and it suddenly brought to rest. Assuming no heat is lost to the surroundings, its temperature increases by 

  • fraction numerator left parenthesis straight gamma minus 1 right parenthesis over denominator 2 γR end fraction Mv squared straight K
  • fraction numerator γMv squared over denominator 2 straight R end fraction minus straight K
  • fraction numerator left parenthesis straight gamma minus 1 right parenthesis over denominator 2 γR end fraction Mv squared straight K
  • fraction numerator left parenthesis straight gamma minus 1 right parenthesis over denominator 2 left parenthesis straight gamma plus 1 right parenthesis straight R end fraction Mv squared straight K

Solution

C.

fraction numerator left parenthesis straight gamma minus 1 right parenthesis over denominator 2 γR end fraction Mv squared straight K

As no heat is lost, therefore,
Loss of kinetic energy = Gain of internal energy of gas
i.e., 
1 half mv squared space equals space nC subscript straight v increment straight T
rightwards double arrow space 1 half mv squared space equals space straight m over straight M. fraction numerator straight R over denominator straight gamma minus 1 end fraction increment straight T
rightwards double arrow increment straight T space equals space fraction numerator Mv squared space left parenthesis straight gamma minus 1 right parenthesis over denominator 2 straight R end fraction straight K