Question

wanda needed room - temperature butter for a cookie recipe. she took two sticks of butter out of the refrigerator and put them on the counter. each stick had the same amount of butter, but one stick was long and thin, and one stick was short and wide. this table shows how the temperature of each stick of butter changed over 30 minutes.

stick of butter	initial temperature (°c)	final temperature (°c)
long stick of butter	4	12

the next time wanda needs butter for a cookie recipe, she wants it to warm up to room temperature quickly. what should she do to maximize the rate of thermal energy transfer into the stick of butter?
options:
use a short and wide stick of butter
use a long and thin stick of butter
either; the rate of thermal energy transfer is the same whether or not the butter is long or short.

Explanation:

Step1: Calculate temp change for short butter

$\Delta T_{\text{short}} = 9^\circ\text{C} - 3^\circ\text{C} = 6^\circ\text{C}$

Step2: Calculate temp change for long butter

$\Delta T_{\text{long}} = 12^\circ\text{C} - 4^\circ\text{C} = 8^\circ\text{C}$

Step3: Compare thermal transfer rates

The long, thin butter had a larger temperature increase over the same 30 minutes, meaning it absorbed thermal energy faster. To maximize the rate, choose the shape with higher surface area relative to volume, which is long and thin.

Answer:

use a long and thin stick of butter