Problem$-3(20$ pts$)$

The input Temperature T$,$ in Celsius, of separator is related to the output Pressure, in Psi, by the following model in Laplace domain,

$G(s)=\frac{P(s)}{T(s)}=\frac{5}{9S+2}$

If the initial steady state value of $)=(0$ and $P(t=0)=40$ psi. Determine the time required for the pressure to reach $45$ psi if the temperature is suddenly increased to $27C.$