How many degrees of freedom are associated with `2` gram of helium at NTP ? Calculate the amount of heat energy required to raise the temp. Of this amount from `27^(@) C to 127^(@) C`. Given Boltzmann constant `k_(B) = 1.38 xx 10^(-23)` erg `"molecule"^(-1) K^(-1)` and Avogadro's number `=6.02 xx 10^(23)`.

Answer

`9.03 xx 10^(23)`, `623.1J`

Explanation

Number of molecules in 2 g of He
`=(6.02 xx 10^(23) xx2)/(4) = 3.01 xx 10^(23)`
Each molecule of (monoatomic) He has 3 degree of freedom
`:.` Total no.of degree of freedom
` n = 3 xx 3.01 xx 10^(23) = 9.03 xx 10^(23)`
At `(27+273)K = 300 K`, energy associated with 2 g of He
`E_(1) = n/2 kT = (9.03 xx 10^(23))/(2) xx 1.38 xx 10^(-23) xx 400`
`= 2492.3 J`
Hence energy required to raise the temperature of He
`=E_(2) -E_(1) = 2492.3 = 1869.2 = 623.1J`