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