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Most Important Selected Qs for JEE AdvancedChemistryStates of Matter

A certain gas has the equation of state, P = RT V _ m - bT - a V _ m ^3 . Where a and b are constants characteristic of the gas. Choose the incorrect relationship(s). [ P _ c , V _ c and T _ c are critical pressure, volume and temperature respectively]

Options

  1. Aa = R T _c V _c^2 3
  2. Bb= V_c 2 T_c
  3. Ca = 4 R T _ e V _ c 3
  4. Db = V _ c 3 ~T _ c

Correct answer

D. b = V _ c 3 ~T _ c

Step-by-step solution

aligned & P= R T V_m-b T - a V_m^3 & ( d P d V_m )_T=- R T (V_m-b T )^2 + 3 a V_m^4 aligned Under critical condition ( d P d V_m )_T=- R T (V_m-b T )^2 + 3 a V_m^4 =0 ...(i) ( d^2 P d V_m^2 )_T=+ 2 R T (V_m-b T )^3 - 12 a V_m^5 =0 ...(ii) On solving (i) and (ii), we get a= 4 R T_c V_c^2 3 and b= V_c 2 T_c

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