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Calculate the amount of heat in BTU required to change the temperature of 10 lb of copper from [tex]$100^{\circ} F$[/tex] to [tex]$150^{\circ} F$[/tex]. The specific heat of copper is [tex]$0.09 \, BTU / lb \cdot \degree F$[/tex].

Select one:
A. [tex]10 \, lb \times 50^{\circ} F \times 0.09 \, BTU / lb \cdot \degree F = 45 \, BTU[/tex]
B. [tex]10 \, lb \times 50^{\circ} F = 500 \, BTU[/tex]
C. [tex]10 \, lb \times 0.09 \, BTU / lb \cdot \degree F = 0.9 \, BTU[/tex]
D. The amount of heat required cannot be calculated using the information given.


Sagot :

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]