A sample of sand initially at 22.3°C absorbs 1.34 x 10^3 J of heat. The final temperature of sand is 67.8 °C. What is the (in g) of sand in the sample? Round to the nearest whole number.
q = mcdT
1.4E3J = mass sand*specific heat sand*(Tfinal-Tinitial). You need to know the specific heat of the sand. Then plug in the numbers and solve for mass sand.
To solve this problem, we can use the specific heat capacity formula:
q = m × c × ΔT
where:
q is the amount of heat absorbed or released,
m is the mass of the substance,
c is the specific heat capacity of the substance, and
ΔT is the change in temperature.
In this case, we know:
q = 1.34 × 10^3 J,
ΔT = 67.8 °C - 22.3 °C = 45.5 °C, and
c for sand is typically around 0.84 J/g°C.
We need to find the mass of the sand (m). Rearranging the formula, we get:
m = q / (c × ΔT)
Substituting the values, we have:
m = 1.34 × 10^3 J / (0.84 J/g°C × 45.5 °C)
m ≈ 36.9 g
Therefore, the mass of the sand in the sample is approximately 37 grams when rounded to the nearest whole number.
To determine the mass of the sand, we can use the equation:
q = mcΔT
Where:
q = heat absorbed by the sand (J)
m = mass of the sand (g)
c = specific heat capacity of sand (J/g°C)
ΔT = change in temperature of the sand (°C)
First, we need to calculate ΔT:
ΔT = final temperature - initial temperature
ΔT = 67.8°C - 22.3°C
ΔT = 45.5°C
Now we can rearrange the equation to solve for the mass of the sand:
m = q / (cΔT)
The specific heat capacity of sand is approximately 0.84 J/g°C (or 0.84 J/gK).
m = 1.34 x 10^3 J / (0.84 J/g°C * 45.5°C)
Calculating:
m = 1.34 x 10^3 J / 38.22 J/g
m ≈ 35.04 g
Therefore, the mass of the sand in the sample is approximately 35 grams (rounded to the nearest whole number).