Final answer:
The specific heat capacity of the unknown metal is calculated using the equation q = m * c * ΔT, where q is the heat gained or lost by the substance, m is the mass of the substance, c is the specific heat capacity of the substance, and ΔT is the change in temperature. By substituting the given values into the equation, we can find that the specific heat capacity of the metal is 0.268 J/g℃.
Step-by-step explanation:
The specific heat capacity of a substance is the amount of heat required to raise the temperature of a given amount of that substance by 1 degree Celsius. To calculate the specific heat capacity of the unknown metal, we can use the formula:
q = m * c * ΔT
Where:
- q is the heat gained or lost by the substance
- m is the mass of the substance
- c is the specific heat capacity of the substance
- ΔT is the change in temperature
First, we need to calculate the heat gained or lost by the metal:
qmetal = mmetal * cmetal * ΔTmetal
Then, we calculate the heat gained or lost by the water:
qwater = mwater * cwater * ΔTwater
Since the metal and water reach the same final temperature, the heat gained by the metal is equal to the heat gained by the water:
qmetal = qwater
By substituting the given values into the equation, we can solve for the specific heat capacity of the metal:
mmetal * cmetal * ΔTmetal = mwater * cwater * ΔTwater
cmetal = (mwater * cwater * ΔTwater) / (mmetal * ΔTmetal)
By substituting the given values:
cmetal = (125 g * 4.18 J/(g℃) * (31.0-25.0)℃) / (134.0 g * (31.0-91.0)℃)
cmetal = 0.268 J/g℃
Therefore, the specific heat capacity of the unknown metal is 0.268 J/g℃.