For a perfectly cyrstalline solid C_(p,m)= a T^(3) + bT, where a and b are constants. If C_(p,m) is 0.40 J/K mol at 10K and 0.92 J/K mol at 20K, then molar entropy at 20K is 0.2x xx R joules. Then the value of x is

For a perfectly cyrstalline solid C_(p,m)= a T^(3) + bT, where a and b

1.	For a perfectly cyrstalline solid C_(p,m)= a T^(3) + bT, where a and b are constants. If C_(p,m) is 0.40 J/K mol at 10K and 0.92 J/K mol at 20K, then molar entropy at 20K is 0.2x xx R joules. Then the value of x is
Answer» 0.92 J/K mol 8.66 J/K mol 0.813 J/K mol none of these Solution :`S_(20)- S_(0) = underset(0)OVERSET(20)int (C_(P))/(T) dT = underset(0)overset(20)int (aT^(3) + bT)/(T) dT` `=[(aT^(3))/(3) + bT]_(0)^(20)` `S_(20) = (a)/(3) (20)^(3) + b(20)` `C_(10) = a(10)^(3) + b(10) =0.4` `C_(20) = a(20)^(3) + b(20) = 0.92` `rArr a = 2 xx 10^(-5) , b= 0.038` `rArr S_(20) = (2)/(3) xx 10^(-5) xx (20)^(3) + 0.038 xx 20` = 0.813 J/mol -K