A heat exchanger during operation in a bioprocess has a steady temperature of $90^{\circ} \mathrm{C}$. After completion of its operation, it was shut down and it was observed that the rate of decrease of temperature at any time was directly proportional to the difference $T(t)-30^{\circ} \mathrm{C}$, where $T(t)$ denotes temperature at time $t$. It was observed that it took $30$ min for the temperature to drop to $70^{\circ} \mathrm{C}$. The temperature after $51.5$ min will be $\_\_\_\_$ ${ }^{\circ} \mathrm{C}$. (rounded off to the nearest integer)
