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Chemistry · The first law of thermodynamics: Concept of work, heat, internal energy and enthalpy, heat capacity, molar heat capacity

Root mean square velocity of molecules of a diatomic gas is to be increased to 1

Root mean square velocity of molecules of a diatomic gas is to be increased to 1.5 times, If the process is done adiabtically, the ratio of initial volume to the final volumes is :

  • A. 2.25
  • B. 4.6
  • C. 5 .6 \)
  • D. 7.5

Step-by-step solution

For an ideal gas, v_rms ∝ √T, so increasing v_rms by 1.5 times implies T increases by (1.5)² = 2.25 times. For an adiabatic process, TV^(γ-1) = constant. For diatomic gas, γ = 7/5 = 1.4, so γ-1 = 0.4. Hence (V_i/V_f)^(0.4) = 2.25, so V_i/V_f = (2.25)^(1/0.4) = (2.25)^(2.5) = (3/2)^5 = 243/32 ≈ 7.59 ≈ 7.5.
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