Final answer:
To find the mass of a sample with a specific heat of 0.96 cal/g°C, releasing 12 calories with a 5°C temperature change, we rearrange the heat transfer formula and calculate to find the sample has a mass of 2.5 g, which does not match the provided options.
Step-by-step explanation:
The question asks for the mass of a sample with a specific heat of 0.96 cal/g°C that releases 12 calories as its temperature changes from 25°C to 20°C. To find this mass, we use the formula for heat transfer q = m • c • ΔT, where q is the heat transfer in calories, m is the mass in grams, c is the specific heat capacity, and ΔT is the temperature change.
First, we calculate the temperature change (ΔT):
25°C - 20°C = 5°C.
Next, we arrange the formula to solve for mass (m):
m = q / (c • ΔT).
Insert the known values:
m = 12 cal / (0.96 cal/g°C • 5°C).
Perform the calculation:
m = 12 cal / (4.8 cal/g), which simplifies to m = 2.5 g.
Therefore, the mass of the sample is 2.5 g, which might correspond to option C) 12.5 g if there is a typo, but without any typo, none of the options provided (A, B, D) is correct.