To solve this problem, let's break it down step-by-step:
1. Identify the specific heat capacity of silver:
The specific heat capacity of silver is [tex]\( 0.235 \, \text{J/(g·°C)} \)[/tex].
2. Convert the initial and final temperatures from Fahrenheit to Celsius:
The formula to convert Fahrenheit (°F) to Celsius (°C) is:
[tex]\[
°C = (°F - 32) \times \frac{5}{9}
\][/tex]
- Initial temperature:
[tex]\[
60°F = (60 - 32) \times \frac{5}{9} = 15.5556°C
\][/tex]
- Final temperature:
[tex]\[
255°F = (255 - 32) \times \frac{5}{9} = 123.8889°C
\][/tex]
3. Calculate the temperature change in Celsius:
The temperature change ([tex]\( \Delta T \)[/tex]) is the difference between the final and initial temperatures:
[tex]\[
\Delta T = 123.8889°C - 15.5556°C = 108.3333°C
\][/tex]
4. Assume an arbitrary mass for the calculation:
Let's assume a mass ([tex]\( m \)[/tex]) of 1 gram, which simplifies our calculation.
5. Apply the formula to calculate the energy needed:
The formula to calculate the energy [tex]\( Q \)[/tex] required to heat the silver is:
[tex]\[
Q = m \times c \times \Delta T
\][/tex]
Where:
- [tex]\( m \)[/tex] is the mass in grams,
- [tex]\( c \)[/tex] is the specific heat capacity in J/(g·°C),
- [tex]\( \Delta T \)[/tex] is the temperature change in °C.
Substituting the values:
[tex]\[
Q = 1 \, \text{g} \times 0.235 \, \text{J/(g·°C)} \times 108.3333 \, \text{°C}
\][/tex]
[tex]\[
Q = 25.4583 \, \text{J}
\][/tex]
That's the amount of energy needed to heat a piece of silver from 60°F to 255°F. Therefore, the energy required is approximately 25.46 Joules.
