The molar heat capacity of a certain substance varies with temperature according to the given equation
`C=27.2+(4xx10^-3)T`
The heat necessary to change the temperature of 2 mol of the substance from 300 K to 700 K is

Options

A. `3.46xx10^4J`
B. `2.33xx10^3J`
C. `3.46xx10^3J`
D. `2.33xx10^4J`

Answer

D

Explanation

Initial temperature, `T_1=300K`
Final temperature `T_f=700K`
`Q=int_(300)^(700)nCdT=int_(300)^(700)2xx(27.2+4xx10^-3xxT)dT`
`=[54.4T+4xx10^-3T^2]_(300)^(700)`
`=2.33xx10^4J`