To calculate the amount of heat required to change the temperature of 10 lb of copper from [tex]\(100^{\circ} F\)[/tex] to [tex]\(150^{\circ} F\)[/tex], we can use the formula for heat transfer:
[tex]\[ Q = m \cdot c \cdot \Delta T \][/tex]
where:
- [tex]\( Q \)[/tex] is the amount of heat (in BTU).
- [tex]\( m \)[/tex] is the mass of the substance (in pounds).
- [tex]\( c \)[/tex] is the specific heat of the substance (in BTU/lb°F).
- [tex]\( \Delta T \)[/tex] is the change in temperature (in degrees Fahrenheit).
Let's follow the steps to solve this:
1. Identify the mass of copper:
[tex]\[ m = 10 \, \text{lb} \][/tex]
2. Identify the initial and final temperatures and compute the temperature change:
[tex]\[ T_{\text{initial}} = 100^{\circ} F \][/tex]
[tex]\[ T_{\text{final}} = 150^{\circ} F \][/tex]
[tex]\[ \Delta T = T_{\text{final}} - T_{\text{initial}} = 150^{\circ} F - 100^{\circ} F = 50^{\circ} F \][/tex]
3. Identify the specific heat of copper:
[tex]\[ c = 0.09 \, \text{BTU/(lb°F)} \][/tex]
4. Substitute these values into the formula:
[tex]\[ Q = 10 \, \text{lb} \cdot 0.09 \, \text{BTU/(lb°F)} \cdot 50^{\circ} F \][/tex]
5. Calculate the heat required:
[tex]\[ Q = 10 \times 0.09 \times 50 \][/tex]
[tex]\[ Q = 10 \times 4.5 \][/tex]
[tex]\[ Q = 45 \, \text{BTU} \][/tex]
Thus, the amount of heat required is [tex]\( 45 \, \text{BTU} \)[/tex].
Therefore, the correct option is:
A. [tex]\( 10 \, \text{lb} \times 50^{\circ} F \times 0.09 \, \text{BTU/lb} = 45 \, \text{BTU} \)[/tex]
