Question

4. During a cell culture experiment, a student placed a Petri dish initially at 25°C in an incubator at 40°C. It took 4 hrs for the Petri dish to reach 37°C. After the Petri dish reached 37°C, the student took it out of the incubator and placed it in a water bath at 20°C. How long will it take for the Petri dish to reach 30°C? You can assume that for both processes, the heat transfer can be modeled by Q--k (T- Tamb), where Tamb Temperature of the surroundings. k is the heat transfer co-efficient. Hint: You do not need a value of k or the mass of the Petri dish to arrive at your final answer]

Answer 1

Heat equation is

$\rho C_p\frac{\partial T}{\partial t} - k*\frac{\partial^2 T}{\partial x^2}=0$

$\frac{\partial T}{\partial t} = \frac{\partial Q}{\partial x}$

where Q = -k (T-Tamb) Change in heat treansfer by convection is constant

$\frac{\partial T}{\partial t} = K$

@ Case-1 K = (37-25)/4 = 3 C/hr

@ Case-2 t = $t = \frac{\Delta T}{K}$ = 7/3 = 3.5 hr