To determine the amount of heat that must be transferred to 55 grams of ice to change its temperature from [tex]\(-13^{\circ} C\)[/tex] to [tex]\(-5.0^{\circ} C\)[/tex], we will follow these steps:
1. Identify the given values:
- Mass of ice ([tex]\(m\)[/tex]) = 55 grams
- Initial temperature ([tex]\(T_i\)[/tex]) = [tex]\(-13^{\circ} C\)[/tex]
- Final temperature ([tex]\(T_f\)[/tex]) = [tex]\(-5.0^{\circ} C\)[/tex]
- Specific heat capacity of ice ([tex]\(c\)[/tex]) = 2.11 [tex]\(\text{J} / \text{g} \cdot \text{ }^{\circ} C\)[/tex]
2. Determine the temperature change ([tex]\(\Delta T\)[/tex]):
[tex]\[
\Delta T = T_f - T_i = (-5.0 - (-13))^{\circ} C = 8^{\circ} C
\][/tex]
3. Apply the formula for heat transfer:
[tex]\[
Q = m \cdot c \cdot \Delta T
\][/tex]
Where:
- [tex]\(Q\)[/tex] is the heat transferred
- [tex]\(m\)[/tex] is the mass of the ice
- [tex]\(c\)[/tex] is the specific heat capacity
- [tex]\(\Delta T\)[/tex] is the temperature change
4. Substitute the known values into the formula:
[tex]\[
Q = 55 \, \text{g} \cdot 2.11 \, \text{J} / \text{g} \cdot \text{ }^{\circ} C \cdot 8 \, ^{\circ} C
\][/tex]
5. Calculate the heat transferred:
[tex]\[
Q = 55 \cdot 2.11 \cdot 8 = 928.4 \, \text{J}
\][/tex]
Therefore, the amount of heat that must be transferred is [tex]\(928.4 \, \text{J}\)[/tex].
Based on the answer choices provided:
A. 930 J
B. 3.3 J
C. 580 J
D. 15 J
Because [tex]\(928.4 \, \text{J}\)[/tex] is closest to [tex]\(930 \, \text{J}\)[/tex], the correct answer is:
A. 930 J
