Let's determine the final temperature of a wooden block that starts at [tex]\( 23.4^\circ C \)[/tex], given that it loses 759 joules of energy. We need to use the formula for heat transfer:
[tex]\[ Q = m \cdot C \cdot \Delta T \][/tex]
Where:
- [tex]\( Q \)[/tex] is the energy lost (759 joules),
- [tex]\( m \)[/tex] is the mass of the wooden block (27.2 grams),
- [tex]\( C \)[/tex] is the specific heat capacity of wood (1.716 joules/gram degree Celsius),
- [tex]\( \Delta T \)[/tex] is the change in temperature.
First, solve for [tex]\( \Delta T \)[/tex]:
[tex]\[ \Delta T = \frac{Q}{m \cdot C} \][/tex]
Now plug in the given values:
[tex]\[ \Delta T = \frac{759}{27.2 \cdot 1.716} \][/tex]
[tex]\[ \Delta T = \frac{759}{46.6752} \][/tex]
[tex]\[ \Delta T = 16.2613 \][/tex]
This is the temperature change. Since the block is losing energy, the temperature will decrease. So, we subtract this change from the initial temperature to find the final temperature:
[tex]\[ \text{Final Temperature} = \text{Initial Temperature} - \Delta T \][/tex]
[tex]\[ \text{Final Temperature} = 23.4^\circ C - 16.2613^\circ C \][/tex]
[tex]\[ \text{Final Temperature} = 7.1387^\circ C \][/tex]
Next, we need to match this final temperature to the closest given choice:
A. [tex]\( 7.1^\circ C \)[/tex]
B. [tex]\( 10.9^\circ C \)[/tex]
C. [tex]\( 16.3^\circ C \)[/tex]
D. [tex]\( 39.7^\circ C \)[/tex]
The calculated final temperature is [tex]\( 7.1387^\circ C \)[/tex], which is closest to [tex]\( 7.1^\circ C \)[/tex].
Therefore, the correct answer is:
A. [tex]\( 7.1^\circ C \)[/tex]
