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A cylinder of fixed capacity 67.2 litres contains helium gas at st.p.the amount of heat required to raise the temperature of the gas by 15 degree celsius

is(R=8.31 j/mol/k) a.520j b.560.9j c.620j d.621.2j plz explain with solution



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Volume V = 67.2 litres  of Helium  at  STP

     ΔT = 15⁰K
1 mole of an ideal gas occupies 22.4 litres at STP.
  So number of moles of Helium gas  n = 67.2/22.4 = 3

we know that
     γ = ratio of specific heats for an ideal mono atomic gas = 5/3
    C_p = heat capacity at constant pressure for a mono atomic gas = 5/2 R    
   C_v = heat capacity at constant volume for a mono atomic gas = 3/2 R

   Change in internal energy = n C_v ΔT 
                                         = 3 * 3/2 * 8.31 J/mol/°K  * 15°K
                                         = 560.925 Joules

 There is no change in the volume and hence no work done in heating the gas by 15 deg.

   Heat supplied = change in internal energy
                         = 560.925 Joules

2 5 2
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