Heat over time comparison question

[Fancy Moses]

I have a fairly basic (I hope) question - please note that the values given are just to make the problem easier to comprehend:

Given:

I'm heating, via convection, a constant sized spherical mass (Let's say m=1g) with a consistent surface area (Let's say SA = 1cm^2) at a constant temperature, Tc, (Let's say Tc = 60ºC) for a time, t = 60 minutes. Let us assume that the mass has an initial temperature (Ti) of 20ºC and after 60 minutes the temperature (Tf) of the mass will equal 50ºC. In a similar scenario (m=1g, SA=1cm^2, Ti=20ºC) how long will it take the mass to equal 50ºC if the new constant ambient temperature equals 100ºC?

Experiment 1:

m = 1g
SA = 1cm^2
Ti = 20ºC
Tc = 60ºC
Tf = 50ºC
t = 60 min

Experiment 2:

m = 1g
SA = 1cm^2
Ti = 20ºC
Tc = 100ºC
Tf = 50ºC
t = ?? min

How would I figure this out? Assuming any necessary chemical or physical properties can be found for the mass.

Any information would be greatly appreciated!

 

[Aaron Barnard]

The answer to this question can be found by using the equation of heat transfer. This equation states that the rate of heat transfer (Q) is equal to the product of the thermal conductivity (k), the area (A), and the temperature difference (ΔT). In other words, Q = kA∆T. In this case, the thermal conductivity (k) and the area (A) remain constant, so the equation simplifies to Q = kA(Tc-Tf). Since we know the values for Q, k, A, Tc, and Tf, we can solve for t, the time it takes to reach the final temperature, by rearranging the equation to t = Q/(kA(Tc-Tf)). Plugging in the given values, we find that t = 60 min.