A sample of iron absorbs 71.1 J of heat, upon which the temperature of the sample increases from 21.5°C to 28.8°C. If the specific heat of iron is 0.450 J/g-K, what is the mass (in grams) of the sample?
use the specific heat units as a guide
71.1 / [m (28.8 - 21.5)] = 0.450
To find the mass of the sample, we can use the formula:
q = m * c * ΔT
Where:
q is the amount of heat absorbed (71.1 J),
m is the mass of the sample (in grams),
c is the specific heat of iron (0.450 J/g-K), and
ΔT is the change in temperature (28.8°C - 21.5°C).
Let's substitute the given values into the formula and solve for m:
71.1 J = m * 0.450 J/g-K * (28.8°C - 21.5°C)
First, let's calculate ΔT:
ΔT = 28.8°C - 21.5°C
= 7.3°C
Now we can substitute this value into the formula:
71.1 J = m * 0.450 J/g-K * 7.3°C
Next, we need to convert the temperature change from Celsius to Kelvin by adding 273.15:
71.1 J = m * 0.450 J/g-K * 7.3 K
Now, let's solve for m by rearranging the equation:
m = 71.1 J / (0.450 J/g-K * 7.3 K)
m = 71.1 J / 3.285 J/g
m ≈ 21.63 g
Therefore, the mass of the sample is approximately 21.63 grams.