To find the amount of heat required to increase the temperature of gold, we can use the formula:
\[ Q = mc\Delta T \]
where:
- \( Q \) is the heat absorbed or released (in joules),
- \( m \) is the mass (in grams),
- \( c \) is the specific heat capacity (in J/g°C),
- \( \Delta T \) is the change in temperature (in °C).
Given:
- \( m = 75.0 \) grams,
- \( c = 0.13 \) J/g°C,
- Initial temperature \( T_i = 150°C \),
- Final temperature \( T_f = 250°C \).
First, we calculate the change in temperature:
\[ \Delta T = T_f - T_i = 250°C - 150°C = 100°C \]
Now we can substitute the values into the equation:
\[ Q = (75.0 , \text{g}) \times (0.13 , \text{J/g°C}) \times (100 , \text{°C}) \]
Calculating \( Q \):
\[ Q = 75.0 \times 0.13 \times 100 \]
\[ Q = 75.0 \times 13 \]
\[ Q = 975 , \text{J} \]
Since none of the options exactly match our calculation, but 980 joules (option B) is the closest.
Therefore, the answer is: B. 980 joules.
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