A solid body of constant heat capacity 1   J   ℃ - 1 is being heated by keeping it in…

A solid body of constant heat capacity 1 J ℃-1 is being heated by keeping it in contact with reservoirs in two ways: (i) Sequentially keeping in contact with 2 reservoirs such that each reservoir supplies the same amount of heat. (ii) Sequentially keeping in contact with 8 reservoirs such that each reservoir supplies the same amount of heat. In both, cases the body is brought from initial temperature 100 K to final temperature 200 K . Entropy change of the body in the two cases respectively is: Note: This question was awarded as a bonus since temperatures were given in centigrade instead of in Kelvin. Proper corrections are made in the question to avoid it.
  1. 2ln2, 8ln2
  2. ln2, 4ln2
  3. ln2, ln2
  4. ln2, 2ln2

Solution

Change in entropy, 

dS=dQTΔQ= heat supplied=CΔT      {C=J °C-1}dQ=CdtdS=CdTTIntergrating both sides∫SiSfdS=C∫dTT  ⇒Sf−Si=ΔS=C.lnT|100200⇒ΔS=C[ln200−ln100]=Cln2and  C=J °C-1⇒  ΔS=ln2Entrpoy change in same for both cases as C is constant, andtemperature change (i.e. from 100 to 200) is same.

Asked in: JEE Main 2015 (04 Apr)

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