Calculate the final temperature if 50 kg of iron is heated from 15.0°C with 5000 kJ of heat. The molar heat capacity of iron is 25.08 J mol–1 K–1.
5E6J = mass Fe x specific heat Fe x (Tfinal-Tinitial)
Thanks!
Here's my answer, but I don;t know if it is correct:
5000KJ=50,000g/55.85 g/mol*25.08j/ mol k *(T high-15C);
5000kj=22452.99 (T high-15C);
(T high-15C)=5000kj/22452.99J mol–1 K–1/1000,
T high-15C=222.69, T high=22.69+15=238C
To calculate the final temperature of the iron, we can use the equation:
Q = mcΔT
Where:
Q is the amount of heat transferred (in joules)
m is the mass of the substance (in kilograms)
c is the specific heat capacity (in joules per kilogram per degree Celsius)
ΔT is the change in temperature (in degrees Celsius or Kelvin)
First, let's convert the given heat transfer from kilojoules to joules:
5000 kJ = 5000 * 1000 J = 5,000,000 J
Next, we'll substitute the given values into the equation:
5,000,000 J = (50 kg) * c * ΔT
Rearranging the equation to solve for ΔT:
ΔT = 5,000,000 J / (50 kg * c)
Note: The molar heat capacity (c) is given in J mol–1 K–1, but we need to convert it to J kg–1 K–1. To do this, we need to know the molar mass of iron. The molar mass of iron (Fe) is approximately 55.845 g mol–1.
Now, let's convert the molar heat capacity to J kg–1 K–1:
c (J kg–1 K–1) = (c (J mol–1 K–1) * molar mass (g)) / 1000
c (J kg–1 K–1) = (25.08 J mol–1 K–1 * 55.845 g mol–1) / 1000
c (J kg–1 K–1) ≈ 1,398.0142 J kg–1 K–1
Substituting the values into the equation:
ΔT = 5,000,000 J / (50 kg * 1,398.0142 J kg–1 K–1)
Calculating ΔT:
ΔT ≈ 71.52 K
Finally, to find the final temperature, we add the change in temperature to the initial temperature:
Final temperature = Initial temperature + ΔT
Final temperature = 15.0°C + 71.52 K
Remember to convert the temperature to the desired unit (either Celsius or Kelvin) based on the question requirements.