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For a monotomic gas at temperature T, ma...

For a monotomic gas at temperature T, match the following columns.
`{:(,"ColumnI",, "ColumnII"),((A),"Speed of sound", (p),sqrt(2RT//M)),((B),"RMS speed of gas molecules",(q),sqrt(8RT//piM)),((C),"Average speed of gas molecules",(r),sqrt(3RT//M)),((D),"Most probable speed of gas molecules",(s),sqrt(5RT//3M)):}`

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Match the parameters given in column I with the expressions given in column II. {:("Column I","Column II"),("1. Pressure of a gas",(i)(KT)/sqrt2pid^2P),("2. RMS speed of gas molecules ",(ii) sqrt((2KT)/m)),("3. Mean free path ",(iii) KT/(sqrt3piP^2)),("4. Most probable speed of gas molecules",(iv) sqrt((3KT)/m)),(,(v)1/3mnv^2),(,(vi)1/3KT):}

{:((1),"The rms speed of gas molecules",(a),1.41sqrt((KT)/(m))),((2),"The average speed of gas molecules",(b),1.28),((3),"The most probable speed of gas molecules",(c),1.73sqrt((KT)/(m))),((4),"Diatomic molecules (High temperature)",(d),1.60sqrt((KT)/(m))):}

An ideal gas consists of a large number of identical molecules. Absolute temperature of the gas is T(in kelvin). Molecular weight of gas is M and R is gas constant. Mathch the proper entries from column-2 to column-1 using the codes given below the columns. {:("Column"-1,"Column"-II),((P)"Root mean square speed of molecules is greater than",(1)sqrt((RT)/(M))),((Q)"Most probable speed of molecues is smaller than",(2)1.5sqrt((RT)/(M))),((R)"Average velocity of a molecule is smaller than",(3)2sqrt((RT)/(M))),((S)"Speed of a molecule may be greater than",(4)2.5sqrt((RT)/(M))):}

An ideal gas consists of a large number of identical molecules. Absolute temperature of the gas is T(in kelvin). Molecular weight of gas is M and R is gas constant. Mathch the proper entries from column-2 to column-1 using the codes given below the columns. {:("Column"-1,"Column"-II),((P)"Root mean square speed of molecules is greater than",(1)sqrt((RT)/(M))),((Q)"Most probable speed of molecues is smaller than",(2)1.5sqrt((RT)/(M))),((R)"Average velocity of a molecule is smaller than",(3)2sqrt((RT)/(M))),((S)"Speed of a molecule may be greater than",(4)2.5sqrt((RT)/(M))):}

Given the ratio of RMS, average and most probable speeds of gas molecules.

Match the following. {:("LIST - 1 ","LIST - 2 "),("(A) Average velcoity ",(1) 3/2 nRT ),("(B) Most probable velocity ",(2) sqrt((8RT)/(pi M)) ),("(C) Kinetic energy of a gas ",(3)sqrt((2RT)/(M)) ),("(D) Kinetic energy of a gas molecule ",(4) sqrt((3RT)/(M)) ),("(E) RMS velocity ",):}

Write the expression for rms speed, average speed and most probable speed of a gas molecule.