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