The molor heat capacity of oxygen gas is given by the expression `C_(v)=a+bT+cT^(2)` where a, b and c are constants. What will be change in internal energy of 8 g of oxygen if it is heated from 200 K to 300 K at constant volume? Assume oxygen as an ideal gas. Given a = 1.2 `JK^(-1)mol^(-1), b = 12.8 xx 10^(-2) JK^(-2) mol^(-1), c = 3.3 xx 10^(-7) JK^(-3)mol^(-1)`.
`{:((1),"1000 J",(2),"950.15 J"),((3),"830.5 J",(4),"315.5 J"):}`

Explanation

`C_(V) = a + bT + cT^(2)`
`dE = nC_(V)dT`
Change in internal energy `=underset(E_(1))overset(E_(2))int dE = n underset(T_(1))overset(T_(2))int (a + bT +cT^(2))dT`
`Delta E = E_(2) - E_(1) = n[aT+(bT^(2))/(2)+(cT^(3))/(3)]_(300)^(300)`
`=n[a(300-200)+(b)/(2)[(300)^(2)-(200)^(2)]+(c)/(3)[(300)^(3)-(200)^(3)]]`
`=(8)/(32)[100a + 2.5 xx 10^(4)b + 6.3 xx 10^(6)C]`
`=(1)/(4)[1.2 xx 100 + 2.5 xx 10^(4) xx 12.8 xx 10^(-2)+ 6.3 xx 10^(6) xx 3.3 xx 10^(-7)]`
= 830.5 J