Two iron bolts, one at 100. °C with a mass of 52.8g, the other at 56.0°C with a mass of 66.8g, are placed in an insulated container. Assuming the heat capacity of the container is negligible, what is the final Celsius temperature inside the container (c of iron = 0.450 J/g·K)?
You need to know the temperature of the air inside the container. I assume you are heating air and not water or some other liquid.
I don't have one, please help
123 C
To find the final Celsius temperature inside the container, we can use the principle of heat transfer between objects. The formula we'll use is:
q = m * c * ΔT
Where:
q is the heat transferred
m is the mass of the object
c is the specific heat capacity
ΔT is the change in temperature
In this case, we have two iron bolts with different initial temperatures. Since the container is insulated, the heat lost by one bolt will be gained by the other. We can set up an equation to represent this:
q1 + q2 = 0
Let's calculate the heat transferred by each bolt separately:
For the first iron bolt:
q1 = m1 * c * ΔT1
q1 = 52.8g * 0.450 J/g·K * (100°C - Tf) (Tf is the final temperature)
For the second iron bolt:
q2 = m2 * c * ΔT2
q2 = 66.8g * 0.450 J/g·K * (Tf - 56.0°C)
Substituting these values into the equation q1 + q2 = 0:
52.8g * 0.450 J/g·K * (100°C - Tf) + 66.8g * 0.450 J/g·K * (Tf - 56.0°C) = 0
Simplifying the equation:
23.76(100 - Tf) + 30.06(Tf - 56) = 0
2376 - 23.76Tf + 30.06Tf - 1683.6 = 0
6.3Tf = 2376 - 1683.6
6.3Tf = 692.4
Tf ≈ 110°C
So, the final Celsius temperature inside the container is approximately 110°C.