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Answer :
Final answer:
In the given problem, using the formula regarding the specific heat capacity calculation - q=mcΔT, and after modifying it to calculate the difference in temperature ΔT = q/(mc), we find that ∆T is approximately 61.8°C. Thus, the final temperature of the metal will be the initial plus this difference, which gives us 81.8°C.
Explanation:
The physics concept being applied in this context is called specific heat, often used in thermodynamics. The specific heat of a substance refers to the amount of heat per unit mass needed to increase the temperature by one degree Celsius. The equation for this is: q=mcΔT, where q represents heat energy, m is the mass of the matter, c is the specific heat capacity, and ΔT is the change in temperature.
In this example, we're asked to find the final temperature (Tfinal) of the metal. We know that 305J of heat is added, the metal's mass is 38.8g, and its initial temperature (Tinitial) is 20.0°C.
We need to rearrange our equation to solve for ΔT: ΔT = q/(mc). Substituting in the given values, ΔT = 305 J / (38.8 g * 0.128 J/g⋅°C) ≈ 61.8°C. The final temperature in this case would therefore be Tfinal = Tinitial + ΔT = 20.0°C + 61.8°C = 81.8°C.
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