A mass M = 15 g of nitrogen is enclosed in a vessel at temperature T = 300 K. What amount of heat has to be transferred to the gas to increase the root-mean-square velocity of molecules 2 times ?

Explanation

`C = sqrt((3RT)/(M))`
Let the rms speed be doubled at `T'` then
`2C = sqrt((3RT)/(M))`
`:. 4 = (T')/(T) implies T' = 4T = 4 xx 300 = 1200 K`
`:. Delta T = 1200 - 300 = 900 K`
Heat `Delta Q = Delta U ( :' Delta W = 0)`
Therefore,
`Delta Q = (m)/(M) C_(v) Delta T = (m)/(M) xx (R )/(gamma - 1) xx Delta T`
`= (15)/(28) xx (8.3)/((7)/(5) - 1) xx 900`
`= 10004 J ~~ 10 kJ`