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A monoatomic gas is heated at constant volume until its pressure is doubled. It is again heated at constant pressure, until its volume is doubled. Find molar specific heat for the whole process.

A monoatomic gas is heated at constant volume until its pressure is doubled. It is again heated at constant pressure, until its volume is doubled. Find molar specific heat for the whole process.

Grade:12th pass

1 Answers

Khimraj
3007 Points
6 years ago
  ΔQ1  =  n C_v  ΔT      
                   = n C_v  (2T1 - T1) = n C_v * T1
  ΔQ2  =  n C_p ΔT  =  n C_p * (4T1 - 2T1) = 2 n C_p  T1
                     = 2 n γ C_v T1
ΔQ1 + ΔQ2 =     n C_v T1 + 2 n γ C_v T1  =  n T1 (1 + 2 γ) C_v
C_m = [ ΔQ1 + ΔQ2 ] /  [ n ΔT ]
    C_m =  [ n T1 (1 + 2 γ) C_v  ]  / [ n 3 T1 ]
               =  (1 + 2 γ) C_v / 3
For monoatomic gas
C_v = 5/2R
γ = 5/3.
So C_m = (1 + 10/3)*(3/2R)/3 = 13R/6.
Hope it clears.

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