When 24.0 cal of heat is added to 18.5 g of aluminum at 19.0 ∘C, what is the final temperature of the aluminum?
The Correct Answer and Explanation is:
To find the final temperature of aluminum after adding heat, we use the specific heat formula:q=m⋅c⋅ΔTq = m \cdot c \cdot \Delta Tq=m⋅c⋅ΔT
Where:
- qqq is the heat added (in calories)
- mmm is the mass (in grams)
- ccc is the specific heat of aluminum (0.215 cal/g·°C)
- ΔT\Delta TΔT is the change in temperature (final temperature minus initial temperature)
Given:
- Heat added, q=24.0q = 24.0q=24.0 cal
- Mass, m=18.5m = 18.5m=18.5 g
- Specific heat, c=0.215c = 0.215c=0.215 cal/g·°C
- Initial temperature, Ti=19.0T_i = 19.0Ti=19.0 °C
Step 1: Rearranging the formula to solve for ΔT\Delta TΔT
ΔT=qm⋅c\Delta T = \frac{q}{m \cdot c}ΔT=m⋅cqΔT=24.018.5⋅0.215\Delta T = \frac{24.0}{18.5 \cdot 0.215}ΔT=18.5⋅0.21524.0ΔT≈24.03.9775≈6.03 °C\Delta T \approx \frac{24.0}{3.9775} \approx 6.03\ \text{°C}ΔT≈3.977524.0≈6.03 °C
Step 2: Calculate the final temperature
Tf=Ti+ΔT=19.0+6.03=25.03 °CT_f = T_i + \Delta T = 19.0 + 6.03 = 25.03\ \text{°C}Tf=Ti+ΔT=19.0+6.03=25.03 °C
Final Answer:
The final temperature of the aluminum is approximately 25.0 °C
Explanation:
When heat is added to a substance, its temperature increases. The amount of temperature change depends on three factors: the amount of heat added, the mass of the substance, and its specific heat capacity. Specific heat tells us how much heat is required to raise the temperature of one gram of a substance by one degree Celsius. In this case, aluminum has a relatively low specific heat, meaning it does not take a lot of energy to raise its temperature.
By applying the specific heat formula, we first determine the temperature change, which came out to about 6.03 °C. Adding this change to the original temperature of 19.0 °C gives a final temperature of 25.0 °C. This method is a practical way to predict how materials respond to heat in thermal processes.
