To determine which baking sheet will warm up the quickest and thus bake the cookies the fastest, we need to examine the specific heat values of the materials in question. The specific heat of a substance tells us how much energy is needed to raise the temperature of 1 gram of that substance by 1°C. A lower specific heat value means that the material will heat up more quickly when energy is applied.
The specific heats of the materials are provided as follows:
- Treated glass: [tex]\(0.75 \, \text{J/g}^\circ \text{C} \)[/tex]
- Aluminum: [tex]\(0.90 \, \text{J/g}^\circ \text{C} \)[/tex]
- Stainless steel: [tex]\(0.50 \, \text{J/g}^\circ \text{C} \)[/tex]
- Copper: [tex]\(0.39 \, \text{J/g}^\circ \text{C} \)[/tex]
Since the material with the lowest specific heat will warm up the quickest, we need to identify which one has the lowest specific heat value among the given materials.
Let's compare the specific heat values:
- Treated glass: [tex]\(0.75 \, \text{J/g}^\circ \text{C} \)[/tex]
- Aluminum: [tex]\(0.90 \, \text{J/g}^\circ \text{C} \)[/tex]
- Stainless steel: [tex]\(0.50 \, \text{J/g}^\circ \text{C} \)[/tex]
- Copper: [tex]\(0.39 \, \text{J/g}^\circ \text{C} \)[/tex]
Out of these values, the lowest specific heat value is [tex]\(0.39 \, \text{J/g}^\circ \text{C} \)[/tex], which corresponds to Copper.
Therefore, the copper baking sheet will warm up the quickest and is likely to bake the cookies the fastest due to its lower specific heat.
