Physics

Problem

An industrial freezer is set to an ambient temperature of

-20^{\circ}\text{C}

. A container of hot liquid at

80^{\circ}\text{C}

is placed inside. The temperature

T(t)

follows Newton's Law of Cooling:

T(t) = (T_{\text{initial}} - T_{\text{ambient}}) e^{-rt} + T_{\text{ambient}}

. If the decay rate constant

r

0.1\,\text{min}^{-1}

, calculate the temperature of the liquid after

10

minutes. (Use

e^{-1} \approx 0.368

)