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Mechanical Properties Of Fluids

Question
CBSEENPH11020278

One mole of diatomic ideal gas undergoes a cyclic process ABC as shown in the figure. The process BC is adiabatic. The temperatures at A, B and C are 400 K, 800 K and 600 K respectively. Choose the correct statement:

  • The change in internal energy in the process AB is -350 R.

  • The change in internal energy in the process BC is -500 R.

  • The change in internal energy in the whole cyclic process is 250 R.

  • The change in internal energy in the process CA is 700 R.

Solution

D.

The change in internal energy in the process CA is 700 R.

According to first law of thermodynamics, 
(i) change in internal energy from A to B i.e, 
increment straight U subscript AB space equals space nC subscript straight V left parenthesis straight T subscript straight B minus straight T subscript straight A right parenthesis space equals space 1 space straight x space fraction numerator 5 straight R over denominator 2 end fraction left parenthesis 800 minus 400 right parenthesis space equals space 1000 straight R
increment straight U subscript BC space equals space nC subscript straight V left parenthesis straight T subscript straight C minus straight T subscript straight B right parenthesis space equals space 1 space straight x space fraction numerator 5 straight R over denominator 2 end fraction left parenthesis 600 minus 400 right parenthesis space equals space minus 500 straight R
increment straight U subscript Total space equals space 0
increment straight U subscript CA space equals space nC subscript straight V left parenthesis straight T subscript straight A minus straight T subscript straight C right parenthesis space equals space 1 space straight x space fraction numerator 5 straight R over denominator 2 end fraction left parenthesis 400 minus 600 right parenthesis space equals space minus 500 straight R space