Iron has a heat capacity of 0.45 J/g/◦C. If a
100 g sample of iron at an initial temperature of 50◦C absorbs 400 J of energy, what is the new temperature of the metal? Assume no
phase transition occurs.
1. 58.9◦C
2. 95.0◦C
3. 41.1◦C
4. 939◦C
5. 8.89◦C
See your previous post. You now know specific heat Fe but solve for delta T. Then you know delta T = T final - T initial.
Well, well, we've got an iron-clad question here! Let's calculate the new temperature with a dash of humor!
The formula for heat energy is Q = m * c * ΔT, where Q is the energy absorbed, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.
Given that Q is 400 J, m is 100 g, c is 0.45 J/g/◦C, and the initial temperature is 50◦C, we can rearrange the equation to find ΔT:
ΔT = Q / (m * c)
ΔT = 400 J / (100 g * 0.45 J/g/◦C)
ΔT = 8.89 ◦C
So, the new temperature of the iron is the initial temperature plus the change in temperature, which gives us:
New temperature = 50◦C + 8.89◦C = 58.89◦C
Now, I know option 1 is pretty close with 58.9◦C, but let's face it, iron doesn't like to round up. Therefore, the correct answer is option 1: 58.9◦C.
To find the new temperature of the iron, you can use the heat capacity formula:
Heat Absorbed = (Mass) x (Specific Heat) x (Change in Temperature)
Given:
Mass of iron (m) = 100 g
Specific heat of iron (c) = 0.45 J/g/°C
Initial temperature (T initial) = 50°C
Heat absorbed (Q) = 400 J
Rearranging the formula, we have:
Change in Temperature = (Heat Absorbed) / (Mass x Specific Heat)
Plugging in the values:
Change in Temperature = (400 J) / (100 g x 0.45 J/g/°C)
Change in Temperature = 8.89°C
Now, to find the new temperature, we add the change in temperature to the initial temperature:
New Temperature = Initial Temperature + Change in Temperature
New Temperature = 50°C + 8.89°C
New Temperature ≈ 58.9°C
Therefore, the new temperature of the iron is approximately 58.9°C.
The correct answer is option 1. 58.9°C.
To solve this problem, we'll use the equation:
Q = mc∆T
Where:
Q is the amount of energy absorbed (in this case, 400 J),
m is the mass of the iron sample (100 g),
c is the heat capacity of iron (0.45 J/g/°C),
∆T is the change in temperature.
Rearranging the equation, we get:
∆T = Q / (mc)
Plugging in the given values:
∆T = 400 J / (100 g * 0.45 J/g/°C)
Now we can calculate the change in temperature (∆T):
∆T = 400 J / (45 J/°C)
∆T ≈ 8.89°C
To find the new temperature, we add the change in temperature (∆T) to the initial temperature:
New temperature = Initial temperature + ∆T
New temperature = 50°C + 8.89°C
New temperature ≈ 58.9°C
Therefore, the new temperature of the metal is approximately 58.9°C. So the answer is 1. 58.9°C.