The pressure in a monoatomic gas increases linearly from `4 xx 10^5 Nm^(-2) ` to `8 xx 10^5 Nm^(-2)` when its volume increases from `0.2 m^3 ` to `0.5 m^3`. Calculate the following:
increase in the internal energy,

Explanation

Given that, `P_1 = 4 xx 10^5 N//m^2, P_2 = 8 xx 10^5 N//m^2 , V_1 = 0.2 m^2, V_2 = 0.5 m^3`
For monoatomic gas :`C_v =(R )/(gamma -1) = (3R)/(2) = ( 3 xx 8.3 )/(2) J// "mole `-K
`therefore `Increase in internal energy, `Delta U=nC_v (T_2-T_1) =(C_v )/(R ) (P_2 V_2 -P_1V_1)`
`=( 12.5 )/( 8.3 ) [8 xx 10^5 xx 0.5 - 4 xx 10^5 xx 0.2 ] = 4.8 xx 10^5 J`