Question

how much heat is needed to change the temperature of 3 grams of gold (c = 0.129 \\(\frac{j}{g\degree c}\\)) from 22\\(\degree\\)c to 363\\(\degree\\)c? the amount is expressed to the nearest whole number.
a) 131 joules
b) 132 joules
c) 140 joules
d) 149 joules

Explanation:

Step1: Recall the heat formula

The formula for heat \( Q \) is \( Q = mc\Delta T \), where \( m \) is mass, \( c \) is specific heat, and \( \Delta T \) is temperature change.

Step2: Calculate \( \Delta T \)

\( \Delta T = 362^\circ\text{C} - 22^\circ\text{C} = 340^\circ\text{C} \).

Step3: Substitute values into formula

\( m = 3 \) g, \( c = 0.129 \frac{\text{J}}{\text{g}^\circ\text{C}} \), \( \Delta T = 340^\circ\text{C} \).
\( Q = 3 \times 0.129 \times 340 \).
First, \( 3 \times 0.129 = 0.387 \). Then, \( 0.387 \times 340 = 131.58 \approx 132 \) (rounded to nearest whole number).

Answer:

132 joules (assuming the option with 132 joules is the correct one, e.g., if one option is "132 joules", that's the answer)