Question

What is the specific heat capacity of a metal if it requires 177.5 J to change the temperature of 15.0 g of the metal from 25.00°C to 34.00°C?


a
1.31 J/g°C
b
0.761 J/g°C
c
19.7 J/g°C
d
11.8 J/g°C

Answer 1

The specific heat capacity (c) of a substance can be calculated using the formula:

\[
q = mc\Delta T
\]

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

From the problem, we know:
- \( q = 177.5 \, \text{J} \)
- \( m = 15.0 \, \text{g} \)
- Initial temperature = 25.00°C
- Final temperature = 34.00°C

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

\[
\Delta T = \text{Final temperature} - \text{Initial temperature} = 34.00°C - 25.00°C = 9.00°C
\]

Now we can plug in the values into the formula to solve for \( c \):

\[
177.5 \, \text{J} = 15.0 \, \text{g} \cdot c \cdot 9.00°C
\]

Rearranging the formula to solve for \( c \):

\[
c = \frac{q}{m \Delta T} = \frac{177.5 \, \text{J}}{15.0 \, \text{g} \cdot 9.00°C}
\]

Calculating the denominator:

\[
15.0 \, \text{g} \cdot 9.00°C = 135.0 \, \text{g°C}
\]

Now substitute this back into the equation for \( c \):

\[
c = \frac{177.5 \, \text{J}}{135.0 \, \text{g°C}} \approx 1.31 \, \text{J/g°C}
\]

Thus, the specific heat capacity of the metal is approximately **1.31 J/g°C**.

The correct answer is:

**a. 1.31 J/g°C**