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?
To solve this problem, we can use the equation:
q = m * Cp * ΔT
Where:
q is the amount of energy transferred (in Joules),
m is the mass of the sample (in grams),
Cp is the specific heat capacity of tin (in J/g•°C),
and ΔT is the change in temperature (in °C).
Step 1: Convert the change in temperature to Kelvin
To convert temperatures from Celsius to Kelvin, we add 273.15. So, ΔT = (−10.0°C + 273.15K) - (15.0°C + 273.15K) = 263.15K - 288.15K = -25K
Step 2: Plug the values into the equation and solve for the mass
543J = m * 0.227 J/g•°C * -25K
Step 3: Solve for the mass
m = 543J / (0.227 J/g•°C * -25K)
m = -543J / (0.227 J/g•°C * 25K)
Step 4: Calculate the mass
m ≈ -543J / (5.675 J/g•°C * K)
m ≈ -9.56 g
However, mass cannot be negative, so the mass of the sample is approximately 9.56 grams.
To solve this problem, we can use the formula:
q = m * Cp * ΔT
where:
q is the heat energy released
m is the mass of the sample
Cp is the specific heat capacity of tin
ΔT is the change in temperature
We are given:
Cp = 0.227 J/g•°C
Initial temperature (T1) = 15.0°C
Final temperature (T2) = -10.0°C
Energy released (q) = 543 J
First, let's calculate the change in temperature (ΔT):
ΔT = T2 - T1 = (-10.0°C) - (15.0°C) = -25.0°C
Now, let's rearrange the formula to solve for mass (m):
m = q / (Cp * ΔT)
Substituting the given values:
m = 543 J / (0.227 J/g•°C * (-25.0°C))
Now let's calculate the mass:
m = 543 J / (-5.675 J/g) ≈ -95.56 g
The mass of the sample is approximately -95.56 grams.
Please note that a negative mass does not make sense in this context, so you may have made an error in your calculations or there may be an error in the data provided. Double-check the calculations and data to ensure accuracy.
-543 = mass Sn x specific heat Sn x (Tf-Ti)
Substitute and solve mass Sn.