A spring$-$loaded piston$-$cylinder device contains $mkg$ of an ideal gas. Initially, the spring has no force on the piston and the corresponding pressure, temperature, and volume are P$1,$ T$1,$ and V$1,$ respectively. Heat is transferred to the gas, causing the piston to rise and to compress the spring. At the state $2,$ the corresponding pressure, temperature, and volume are $P2,T2,$ and V $2,$ respectively.

$(9)$ The quantities are given at below. If the ideal gas is a monotonic type, calculate the total internal energy change $U,$

$m=2kg,P1=400$kPa,$T1=150K,V1=0\mathrm{.}1m^3$

$T2=900K,V2=0\mathrm{.}3m^3,Cv=0\mathrm{.}657k\frac{J}{k}g*K$

$$ kJ $.$