To find the mass of water given that [tex]\(0.296 \, \text{J}\)[/tex] of heat causes a [tex]\(0.661 \, ^\circ \text{C}\)[/tex] temperature change, we can use the formula for heat transfer in terms of mass, specific heat capacity, and temperature change:
[tex]\[ Q = m \cdot c \cdot \Delta T \][/tex]
where:
- [tex]\( Q \)[/tex] is the heat added (in Joules),
- [tex]\( m \)[/tex] is the mass of the water (in grams),
- [tex]\( c \)[/tex] is the specific heat capacity of water, which is [tex]\(4.186 \, \text{J/(g}^\circ \text{C)}\)[/tex],
- [tex]\( \Delta T \)[/tex] is the temperature change (in degrees Celsius).
Given values:
- [tex]\( Q = 0.296 \, \text{J} \)[/tex],
- [tex]\( \Delta T = 0.661 \, ^\circ \text{C} \)[/tex],
- [tex]\( c = 4.186 \, \text{J/(g}^\circ \text{C)}\)[/tex].
We need to solve for [tex]\( m \)[/tex]. Rearranging the formula to solve for mass [tex]\( m \)[/tex]:
[tex]\[ m = \frac{Q}{c \cdot \Delta T} \][/tex]
Substitute the known values into the equation:
[tex]\[ m = \frac{0.296 \, \text{J}}{4.186 \, \text{J/(g}^\circ \text{C)} \cdot 0.661 \, ^\circ \text{C}} \][/tex]
Calculate the denominator:
[tex]\[ 4.186 \, \text{J/(g}^\circ \text{C)} \cdot 0.661 \, ^\circ \text{C} = 2.768626 \, \text{J/g} \][/tex]
Now, divide the numerator by the calculated denominator:
[tex]\[ m = \frac{0.296 \, \text{J}}{2.768626 \, \text{J/g}} \][/tex]
[tex]\[ m \approx 0.106977 \, \text{g} \][/tex]
Rounding to three decimal places, we find:
[tex]\[ m \approx 0.107 \, \text{g} \][/tex]
Thus, the mass of water present is approximately [tex]\(0.107 \, \text{g}\)[/tex].
Therefore, the correct answer is:
[tex]\( \boxed{0.107} \, \text{g} \)[/tex]
