To determine the mass of aluminum that absorbs 475 Joules of heat when its temperature increases by 6.2°C, we start with the formula for heat absorption:
\(\[ Q = mc\Delta T \]\)
Where:
- \(\( Q \)\) is the amount of heat absorbed, in Joules.
- \(\( m \)\) is the mass of the substance, in grams.
- \(\( c \)\) is the specific heat capacity of the substance, in Joules per gram per degree Celsius (J/g°C).
- \(\( \Delta T \)\) is the change in temperature, in degrees Celsius (°C).
Given values:
- \(\( Q = 475 \)\) Joules
- \(\( \Delta T = 6.2 \)\) °C
- Specific heat capacity of aluminum, \(\( c = 0.897 \)\) J/g°C
We need to solve for the mass (\(\( m \)\)). Rearrange the formula to solve for \(\( m \)\):
\(\[ m = \frac{Q}{c \Delta T} \]\)
Now, substitute the given values into the equation:
\(\[ m = \frac{475 \text{ Joules}}{0.897 \text{ J/g°C} \times 6.2 \text{ °C}} \]\)
Perform the multiplication in the denominator:
\(\[ 0.897 \text{ J/g°C} \times 6.2 \text{ °C} = 5.5614 \text{ J/g} \]\)
Now, divide the numerator by the calculated denominator:
\(\[ m = \frac{475 \text{ Joules}}{5.5614 \text{ J/g}} = 85.41014852375301 \text{ grams} \]\)
Therefore, the mass of aluminum that absorbs 475 Joules of heat as its temperature increases by 6.2°C is approximately 85.41 grams.
