Q68 / 90 · JEE Main 2019 (09 Jan Shift 2) · Physics

A 15 g mass of nitrogen gas is enclosed in a vessel at a temperature, 27oC. The amount of heat transferred to the gas, so that R.M.S. velocity of molecules is doubled, is about.
R=8.3 J K mole-1

  • A
    14 kJ
  • Correct answer
    B
    10 kJ
  • C
    6 kJ
  • D
    0.9 kJ

Solution

The formula of root-mean-square speed, vrms=3RTM. For doubling the vrms, temperature, should be made 4-time is,  Tf=273+27×4 K=1200 K, the formula of, ∆Q=∆U+WW=0, 
⇒∆Q=∆U=nCV ∆T=1528×52R ∆T
⇒∆Q=1528×52×8.3×1200-300 J≈10 KJ. 

Hence, the correct answer is option: 'B'.

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