To determine which substance would retain the most heat for the longest period of time, we need to compare their specific heat capacities. The specific heat capacity is a measure of the amount of heat required to change the temperature of a given mass of a substance by one degree Celsius. The higher the specific heat capacity, the more heat the substance can store.
Here are the specific heat capacities of the given substances:
1. [tex]\( \text{Al (s)} \)[/tex] : [tex]\( 0.897 \, \text{J/g°C} \)[/tex]
2. [tex]\( \text{H}_2\text{O (s)} \)[/tex] : [tex]\( 2.09 \, \text{J/g°C} \)[/tex]
3. [tex]\( \text{H}_2\text{O (l)} \)[/tex] : [tex]\( 4.18 \, \text{J/g°C} \)[/tex]
4. [tex]\( \text{Sn (s)} \)[/tex] : [tex]\( 0.228 \, \text{J/g°C} \)[/tex]
To determine which substance retains the most heat, we look for the one with the highest specific heat capacity.
From the values given:
- [tex]\( \operatorname{Al (s)} \)[/tex]: [tex]\( 0.897 \, \text{J/g°C} \)[/tex]
- [tex]\( \text{H}_2\text{O (s)} \)[/tex]: [tex]\( 2.09 \, \text{J/g°C} \)[/tex]
- [tex]\( \text{H}_2\text{O (l)} \)[/tex]: [tex]\( 4.18 \, \text{J/g°C} \)[/tex]
- [tex]\( \operatorname{Sn (s)} \)[/tex]: [tex]\( 0.228 \, \text{J/g°C} \)[/tex]
Among these substances, [tex]\( \text{H}_2\text{O (l)} \)[/tex] has the highest specific heat capacity of [tex]\( 4.18 \, \text{J/g°C} \)[/tex]. Therefore, liquid water ([tex]\( \text{H}_2\text{O (l)} \)[/tex]) will retain the most heat for the longest period of time.
