A container is filled with 20 moles of an ideal gas at absolute temperature T. When heat is supplied to gas temperature remains constant but 8 moles dissociate into atoms. Heat energy given to gas is-(1)4RT, (2)6RT, (3)3RT, (4)5RT

Asked by patra04011965 | 16th Mar, 2019, 12:20: PM

Expert Answer:

A container  filled  with n1  = 20 moles of ideal diatomic  gas at  absolute  temperature  T.  when heat  is supplied to  gas  temperature  remains constant  but  n2 = 8  molesdissociated into  atoms.  Heat  energy  given to  gas  is Solution Since  the gas  is  enclosed in  a  vessel,  therefore,  during  heating  process,  volume  of  the  gas remains constant.   Hence,  no  work  is  done  by  the gas.  It  means heat  supplied to the gas is  used to  increase  its  internal energy only.   Initial  internal energy  of the  gas is U1 =n1(5/2 RT ). Since  n  moles get  dissociated into  atoms, therefore,  after heating, vessel  contains  (n1  −  n2)  moles  of diatomic gas  and  2n2  moles  of  a mono-atomic gas. Hence  the internal  energy  for  the  gas, after  heating,  will be  equal to U2 =(n1  −  n2)5/2RT +2n2*3/2RT = 5/2n1RT + n2RT/2
Hence,  the  heat  supplied  is  equal to  the  increase  in  internal energy 
U2-U1 = 4RT

Answered by Ankit K | 16th Mar, 2019, 07:47: PM

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