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Distribution Of Molecular Speeds

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The Maxwell-Boltzmann distribution of molecular speeds in a sample of an ideal gas can be expressed as f=(4)/(sqrt(pi))((m)/(2kT))^(3//2)v^(2)e^(-(mv^(2))/(2kT)).dv Where f represent the fraction of total molecules that have speeds between v and v + dv.m, k and T are mass of each molecule, Boltzmann constant and temperature of the gas. (a) What will be value of int_(v=0)^(v=oo)fdv ? (b) It is given that int_(0)^(oo) v^(3)e^(-av^(2))dv=(1)/(2a^(2)) Find the average speed of gas molecules at temperature T.

The distribution of the molecular velocities of gas molecules at any temperature T is shown below. (The plot below is known as Maxwell's distribution of molecular speeds.) where v is molecular velocity n is number of molecules having velocity v Let us define Delta N_(v) , which is equal to the number of molecules between the velocity range v and v+ Delta v , given by Delta N_(v)=4piNa^(3)e^(-bv^(2))v^(2)Deltav where N is total number of molecules a=sqrt((M_(0))/(2piRT)) and b=(M_(0))/(2RT) R is universal gas constant T is temperature of the gas M_(0) is molecular weight of the gas Answer the following question: SI units of b are

Knowledge Check

  • Following curves are plotted according to Maxwell distribution of molecular speed.

    A
    For He gas, temperature corresponding to I curve is higher than II curve.
    B
    At same temperature, I and II curve may represent `N_2 and O_2` gas respectively.
    C
    Fraction of molecules having `U_(mps)` is more in curve I than curve II.
    D
    I and II curve may represent `O_2(g)` at 300 K and `SO_2(g)` at 500 K respectively.

  • Which one of the following statement is NOT true about the effect of an increase in temperature on the distribution of molecular speed in a gas?

    A
    The area under the distribution curve remains the same as under the lower temperature
    B
    The distribution becomes broader
    C
    The fraction of the molecules with the most probable speed increases
    D
    The most probable speed increases

  • Statement-1 :The area under the maxwell distribution molecular speed curve remains same irrespective of temperature of gas. Statement-2 :The fraction of molecules with most probable speed increases with increases of temperature.

    A
    Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1
    B
    Statement-1 is True, Statement-2 is True, Statement-2 is NOT a correct explanation for Statement-1
    C
    Statement-1 is True, Statement-2 is False.
    D
    Statement-1 is False, Statement-2 is True.

    • Similar Questions

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    The distribution of the molecular velocities of gas molecules at any temperature T is shown below. (The plot below is known as Maxwell's distribution of molecular speeds.) where v is molecular velocity n is number of molecules having velocity v Let us define Delta N_(v) , which is equal to the number of molecules between the velocity range v and v+ Delta v , given by Delta N_(v)=4piNa^(3)e^(-bv^(2))v^(2)Deltav where N is total number of molecules a=sqrt((M_(0))/(2piRT)) and b=(M_(0))/(2RT) R is universal gas constant T is temperature of the gas M_(0) is molecular weight of the gas Answer the following question: SI units of a are

    The distribution of the molecular velocities of gas molecules at any temperature T is shown below. (The plot below is known as Maxwell's distribution of molecular speeds.) where v is molecular velocity n is number of molecules having velocity v Let us define Delta N_(v) , which is equal to the number of molecules between the velocity range v and v+ Delta v , given by Delta N_(v)=4piNa^(3)e^(-bv^(2))v^(2)Deltav where N is total number of molecules a=sqrt((M_(0))/(2piRT)) and b=(M_(0))/(2RT) R is universal gas constant T is temperature of the gas M_(0) is molecular weight of the gas Answer the following question: If (P)/(P_(c))=P_(r) , (T)/(T_(c))=T_(r) , and (V_(m))/(V_(m,c))=V_(r) where

    Explain Maxwell distribution of molecular speed with necessary graph.

    Which one of the following statement is not true about the effect of an increase in temperature on the distribution of molecular speed of gas ? .

    The Maxwell-Boltzmann distribution law of molecular speeds is graphically represented as The curve has which of the following characteristics ?.

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