To solve for the mass of the substance, we use the formula for heat transfer:
[tex]\[ Q = mcΔT \][/tex]
where:
- [tex]\( Q \)[/tex] is the amount of heat added (in joules),
- [tex]\( m \)[/tex] is the mass of the substance (in grams),
- [tex]\( c \)[/tex] is the specific heat capacity (in joules per gram per degree Celsius),
- [tex]\( ΔT \)[/tex] is the change in temperature (in degrees Celsius).
Given:
- [tex]\( Q = 350 \)[/tex] joules,
- [tex]\( c = 1.2 \)[/tex] joules per gram per degree Celsius,
- The initial temperature [tex]\( T_i = 10.0^{\circ} C \)[/tex],
- The final temperature [tex]\( T_f = 30.0^{\circ} C \)[/tex].
First, calculate the change in temperature [tex]\( ΔT \)[/tex]:
[tex]\[ ΔT = T_f - T_i = 30.0 - 10.0 = 20.0^{\circ} C \][/tex]
Next, rearrange the formula to solve for the mass [tex]\( m \)[/tex]:
[tex]\[ m = \frac{Q}{cΔT} \][/tex]
Substitute the given values into the formula:
[tex]\[ m = \frac{350 \, \text{joules}}{1.2 \, \text{J/g} \cdot 20.0^{\circ} C} \][/tex]
[tex]\[ m = \frac{350}{1.2 \times 20.0} \][/tex]
[tex]\[ m = \frac{350}{24} \][/tex]
[tex]\[ m ≈ 14.583333333333334 \, \text{grams} \][/tex]
Therefore, the mass of the substance is approximately [tex]\( 14.58 \)[/tex] grams. The closest answer is:
15 grams.
