a$)$ A potato slice, initially at a uniform temperature of $70C,$ is placed in an

environment where the surrounding air is at $25C.$ The convective heat transfer

coefficient between the air and the surface of the potato is $10\frac{W}{m^2}*K.$ The potato

slice is assumed to have the following properties: Density $=800k\frac{g}{m^{-}},$ Specific heat

capacity $=3400Jkg*K.$ Surface area of the slice $=0\mathrm{.}01m^3,$ Volume of the

slice $=0\mathrm{.}0001m^3.$

Using the lumped capacitance method, determine the temperature of the potato slice

after $500$ seconds. Assume that the lumped capacitance model is valid and that the

temperature throughout the potato slice is uniform during the cooling process.

Also, use the analytical approximation method and the simplified solution for large

times to calculate the temperature of the potato slice after $500$ seconds.