To determine the heat capacity of a piece of wood given the information provided, we can follow these steps:
1. Identify the given values:
- Mass of the wood ([tex]\(m\)[/tex]) = 1500 grams
- Heat absorbed ([tex]\(Q\)[/tex]) = 67500 joules
- Initial temperature ([tex]\(T_i\)[/tex]) = 32°C
- Final temperature ([tex]\(T_f\)[/tex]) = 57°C
2. Calculate the change in temperature:
[tex]\[
\Delta T = T_f - T_i
\][/tex]
Substitute the values:
[tex]\[
\Delta T = 57°C - 32°C = 25°C
\][/tex]
3. Use the formula for specific heat capacity:
The formula to calculate the specific heat capacity [tex]\(c\)[/tex] is:
[tex]\[
Q = m \cdot c \cdot \Delta T
\][/tex]
Solving for [tex]\(c\)[/tex]:
[tex]\[
c = \frac{Q}{m \cdot \Delta T}
\][/tex]
4. Plug in the given values:
[tex]\[
c = \frac{67500 \text{ joules}}{1500 \text{ grams} \times 25°C}
\][/tex]
5. Perform the division:
[tex]\[
c = \frac{67500}{37500} = 1.8 \text{ J/g°C}
\][/tex]
Therefore, the heat capacity of the piece of wood is [tex]\(1.8 \text{ J/g°C}\)[/tex].
So, the correct answer is:
- a. 1.8 J/g˚C
