Question

What amount of energy in joules is required to raise the temperature of 5.00 g of silver from 25.0°C to 27.5°C? (The specific heat of silver is 0.24 J/g°C.)
A. 12.5 J
B. 1.2 J
C. 0.14 J
D. 3.0 J

Answer 1

To calculate the amount of energy required to raise the temperature of a substance, we can use the formula:

\[
q = m \cdot c \cdot \Delta T
\]

where:
- \( q \) is the heat energy (in joules),
- \( m \) is the mass of the substance (in grams),
- \( c \) is the specific heat capacity (in J/g°C), and
- \( \Delta T \) is the change in temperature (in °C).

Given:
- Mass of silver, \( m = 5.00 \, \text{g} \)
- Specific heat of silver, \( c = 0.24 \, \text{J/g°C} \)
- Initial temperature, \( T_i = 25.0 \, \text{°C} \)
- Final temperature, \( T_f = 27.5 \, \text{°C} \)

First, we need to calculate the change in temperature (\( \Delta T \)):

\[
\Delta T = T_f - T_i = 27.5 \, \text{°C} - 25.0 \, \text{°C} = 2.5 \, \text{°C}
\]

Now we can plug the values into the formula:

\[
q = m \cdot c \cdot \Delta T = 5.00 \, \text{g} \cdot 0.24 \, \text{J/g°C} \cdot 2.5 \, \text{°C}
\]

Calculating:

\[
q = 5.00 \cdot 0.24 \cdot 2.5 = 3.00 \, \text{J}
\]

Thus, the amount of energy required is:

\[
\boxed{3.0 \, \text{J}}
\]

The correct answer is D. 3.0 J.