A sample of tin (Cp = 0.227 J/g•°C) is placed in a freezer. Its temperature decreases from 15.0°C to −10.0°C as it releases 543 J of energy. What is the mass of the sample? Round your answer to three significant figures.
To find the mass of the sample, we can use the equation:
q = m * Cp * ΔT
Where:
q = energy released (in Joules)
m = mass of the sample (in grams)
Cp = specific heat capacity of tin (in J/g•°C)
ΔT = change in temperature (in °C)
Step 1: Plug in the given values:
q = 543 J
Cp = 0.227 J/g•°C
ΔT = (final temperature) - (initial temperature) = (-10.0°C) - (15.0°C) = -25.0°C
Step 2: Rearrange the equation to solve for mass (m):
m = q / (Cp * ΔT)
Step 3: Substitute the values:
m = 543 J / (0.227 J/g•°C * -25.0°C)
Step 4: Calculate the mass:
m = -543 J / (0.227 J/g•°C * 25.0°C) = -543 J / (-5.675 J/g) ≈ 95.672 g
Step 5: Round the answer to three significant figures:
m ≈ 95.7 g
Therefore, the mass of the sample is approximately 95.7 grams.
To find the mass of the tin sample, we can use the equation:
Q = m * Cp * ΔT
Where:
Q is the energy released by the tin sample (543 J),
m is the mass of the tin sample (unknown),
Cp is the specific heat capacity of tin (0.227 J/g•°C), and
ΔT is the change in temperature (from 15.0°C to -10.0°C).
First, let's calculate the change in temperature (ΔT):
ΔT = final temperature - initial temperature
ΔT = -10.0°C - 15.0°C
ΔT = -25.0°C
Now we can rearrange the equation to solve for mass (m):
m = Q / (Cp * ΔT)
Substituting the known values:
m = 543 J / (0.227 J/g•°C * -25.0°C)
The negative sign in the denominator accounts for the decrease in temperature. Now we can solve for mass:
m = 543 J / (-5.675 J/g)
m ≈ -95.40 g
Since mass cannot be negative, we must take the absolute value of the result:
m ≈ 95.40 g
Rounding to three significant figures, the mass of the tin sample is 95.4 g.
mass * .227 * (15.0 - 10.0) = 543
answer is in grams