Question

steve prepared two pies and put them next to each other in the oven. the pies were identical, but one was in a glass pie pan and one was in a ceramic pie pan. this table shows how the temperature of each pie changed over 20 minutes.

pie	initial temperature (°c)	final temperature (°c)
pie in the glass pan	21	51

the next time steve puts a pie in the oven, he wants the pie to warm up quickly. what should he do to maximize the rate of thermal energy transfer into the pie?

options:

• use the ceramic pan
• use the glass pan
• either; the rate of thermal energy transfer is the same whether the pie is in the glass or ceramic pan

Explanation:

Step1: Calculate temperature change for ceramic pan

The initial temperature of the pie in the ceramic pan is \(25^\circ C\) and the final temperature is \(55^\circ C\). The temperature change \(\Delta T_{ceramic}\) is calculated as \(55 - 25 = 30^\circ C\) over 20 minutes.

Step2: Calculate temperature change for glass pan

The initial temperature of the pie in the glass pan is \(21^\circ C\) and the final temperature is \(51^\circ C\). The temperature change \(\Delta T_{glass}\) is calculated as \(51 - 21 = 30^\circ C\) over 20 minutes? Wait, no, wait. Wait, no, let's recalculate. Wait, \(55 - 25 = 30\), \(51 - 21 = 30\)? Wait, that can't be. Wait, maybe I made a mistake. Wait, no, the time is 20 minutes for both. Wait, but the rate of temperature change (which is related to thermal energy transfer rate) can be calculated as \(\frac{\Delta T}{t}\). For ceramic pan: \(\frac{55 - 25}{20}=\frac{30}{20} = 1.5^\circ C\) per minute. For glass pan: \(\frac{51 - 21}{20}=\frac{30}{20}=1.5^\circ C\) per minute? Wait, that's the same? But that contradicts. Wait, no, maybe the initial temperatures are different. Wait, the pies are identical, but the pans are different. Wait, maybe the key is the thermal conductivity of the pan. Ceramic is a better conductor of heat than glass? Wait, no, actually, glass has lower thermal conductivity than ceramic? Wait, no, ceramic is a better insulator? Wait, no, maybe I got it wrong. Wait, the pie in the ceramic pan had a higher final temperature. Wait, initial temperature of ceramic pan pie is 25, glass is 21. Final temperature ceramic is 55, glass is 51. So the change in temperature for ceramic is \(55 - 25 = 30\), for glass is \(51 - 21 = 30\). But the time is 20 minutes. So the rate of temperature increase is the same? But that can't be. Wait, maybe the question is about which pan allows more thermal energy transfer. Wait, the pie in the ceramic pan reached a higher final temperature, so the rate of thermal energy transfer into the pie is higher when using the ceramic pan. So to maximize the rate of thermal energy transfer, Steve should use the ceramic pan.

Answer:

use the ceramic pan