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Answer :
To determine the change in temperature when adding 35,000 Joules of heat to a 0.5 kg sample of copper, we'll use the formula for calculating heat transfer:
[tex]\[ Q = mc\Delta T \][/tex]
Where:
- [tex]\( Q \)[/tex] is the heat added in Joules (35,000 Joules),
- [tex]\( m \)[/tex] is the mass in kilograms (0.5 kg),
- [tex]\( c \)[/tex] is the specific heat capacity (385 J/kg°C for copper),
- [tex]\( \Delta T \)[/tex] is the change in temperature in degrees Celsius.
We need to rearrange this formula to solve for the change in temperature, [tex]\(\Delta T\)[/tex]:
[tex]\[ \Delta T = \frac{Q}{mc} \][/tex]
Substitute the given values into the formula:
[tex]\[ \Delta T = \frac{35,000}{0.5 \times 385} \][/tex]
Calculate the product in the denominator:
[tex]\[ 0.5 \times 385 = 192.5 \][/tex]
Then divide the Joules by this product:
[tex]\[ \Delta T = \frac{35,000}{192.5} \approx 181.82 \][/tex]
Rounding that result to the nearest whole number, the change in temperature is approximately 182 degrees Celsius.
So, the choice that best represents the solution is:
182 degrees.
[tex]\[ Q = mc\Delta T \][/tex]
Where:
- [tex]\( Q \)[/tex] is the heat added in Joules (35,000 Joules),
- [tex]\( m \)[/tex] is the mass in kilograms (0.5 kg),
- [tex]\( c \)[/tex] is the specific heat capacity (385 J/kg°C for copper),
- [tex]\( \Delta T \)[/tex] is the change in temperature in degrees Celsius.
We need to rearrange this formula to solve for the change in temperature, [tex]\(\Delta T\)[/tex]:
[tex]\[ \Delta T = \frac{Q}{mc} \][/tex]
Substitute the given values into the formula:
[tex]\[ \Delta T = \frac{35,000}{0.5 \times 385} \][/tex]
Calculate the product in the denominator:
[tex]\[ 0.5 \times 385 = 192.5 \][/tex]
Then divide the Joules by this product:
[tex]\[ \Delta T = \frac{35,000}{192.5} \approx 181.82 \][/tex]
Rounding that result to the nearest whole number, the change in temperature is approximately 182 degrees Celsius.
So, the choice that best represents the solution is:
182 degrees.
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