To find the change in temperature (∆T) for the silicon when 125 J of energy is released, we can use the formula derived from the relationship between heat energy, mass, specific heat capacity, and the change in temperature:
[tex]\[ q = m \cdot c \cdot \Delta T \][/tex]
Where:
- [tex]\( q \)[/tex] is the heat energy (in Joules, J)
- [tex]\( m \)[/tex] is the mass of the substance (in grams, g)
- [tex]\( c \)[/tex] is the specific heat capacity (in J/(g·°C))
- [tex]\( \Delta T \)[/tex] is the change in temperature (in °C)
Given values:
- [tex]\( q = 125 \, \text{J} \)[/tex]
- [tex]\( m = 25.0 \, \text{g} \)[/tex]
- Specific heat capacity of silicon, [tex]\( c_{\text{Si}} = 0.170 \, \text{J/(g·°C)} \)[/tex]
We need to find the change in temperature, [tex]\( \Delta T \)[/tex].
First, let's rearrange the formula to solve for [tex]\( \Delta T \)[/tex]:
[tex]\[ \Delta T = \frac{q}{m \cdot c} \][/tex]
Substitute the given values into the equation:
[tex]\[ \Delta T = \frac{125}{25.0 \times 0.170} \][/tex]
Calculate the denominator:
[tex]\[ 25.0 \times 0.170 = 4.25 \][/tex]
Now, divide the heat energy by this value:
[tex]\[ \Delta T = \frac{125}{4.25} \][/tex]
Perform the division:
[tex]\[ \Delta T \approx 29.41 \, ^\circ\text{C} \][/tex]
So, the change in temperature for the silicon when 125 J of energy is released is approximately:
[tex]\[ \Delta T \approx 29.41 \, ^\circ\text{C} \][/tex]
