Help a Lost Student: Calculating Heat Transfer in H2O

[wunderkind]

I am lost on this homework assignment, and I am really hoping that you guys can help me out. Here goes:
A 500.0-g Fe bar at 212 degrees C is placed in 2.0L of H20 at 24.0 degrees C. What will be the change in temperature of the H2O? (if is assumed that no heat is lost to the surroundings)

I would really appreciate any help you can provide.

 

[chroot]

The heat lost by the iron bar is the same as the heat gained by the water.

Do you know how to find the temperature change of a material when it loses or gains a given amount of heat?

- Warren

 

[ravenprp]

Sure, I would be happy to help you with this problem. First, we need to understand the concept of heat transfer. Heat transfer is the movement of thermal energy from one object to another due to a difference in temperature. In this case, we have a hot iron bar being placed in cooler water, so heat will transfer from the iron bar to the water until both reach the same temperature.

To solve this problem, we can use the formula Q = mCΔT, where Q is the heat transferred, m is the mass of the substance, C is the specific heat capacity, and ΔT is the change in temperature.

We can start by finding the heat transferred from the iron bar to the water. The mass of the iron bar is given as 500.0 g. We can assume the specific heat capacity of iron to be 0.45 J/g°C. The initial temperature of the iron bar is 212°C, and the final temperature will be the same as the water, which we need to find. So, we have:

Q = (500.0 g)(0.45 J/g°C)(212°C - T)
Q = 95,400 J - 225 JT

Next, we need to find the heat absorbed by the water. The mass of the water is given as 2.0L, which is equivalent to 2000 g. The specific heat capacity of water is 4.18 J/g°C. The initial temperature of the water is 24°C, and the final temperature will be the same as the iron bar, which we also need to find. So, we have:

Q = (2000 g)(4.18 J/g°C)(T - 24°C)
Q = 8360T - 200,160 J

Since we know that the heat transferred from the iron bar to the water is equal to the heat absorbed by the water, we can set these two equations equal to each other and solve for T.

95,400 J - 225 JT = 8360T - 200,160 J
93,800 J = 8585 T
T = 10.91°C

Therefore, the final temperature of the water will be 10.91°C, which means there will be a decrease in temperature of 13.09°C.

I hope this helps you understand how to calculate heat transfer and solve this problem. If you have any further questions,