For a particular intensity of incident light on a silicon $pn$ junction solar cell, the photocurrent density $(J_L)$ is $2.5 mA/cm^2$ and the open-circuit voltage ($V_{oc}$) is $0.451$ V. Consider thermal voltage ($V_T$) to be $25$ mV. If the intensity of the incident light is increased by $20$ times, assuming that the temperature remains unchanged, $V_{oc}$ (in volts) will be ____________