What is the Equilibrium Temperature When Brass Meets Water?

[Damien20]

Homework Statement

50 grams of brass shot are heated to 200C° and dropped into a 50-g aluminum cup containing 160-g of water. The temperature of the cup and water are 20 C°. what is the equilibrium temperature.

Homework Equations

mcΔT=mcΔT

The Attempt at a Solution

I've made a few different attempts but all of them are horribly wrong and long.

If anyone can drop a hint or a formula to work off that would be awesome.

 

[kuruman]

There are three items that reach thermal equilibrium, brass, aluminum and water. Assuming that no heat is lost to the environment, there should be three terms of the mcΔT type adding up to zero. The brass term will turn out negative because the temperature of the brass will have to drop. You need to look up the specific heats for the three items if you don't already have them.

 

[tomcue]

I would approach this problem by first considering the principles of thermal equilibrium. Thermal equilibrium occurs when two objects or systems are at the same temperature and there is no net transfer of heat between them. In this problem, the brass shot and the water in the cup will eventually reach thermal equilibrium.

To solve for the equilibrium temperature, we can use the equation Q = mcΔT, where Q is the heat transferred, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.

First, we can calculate the heat transferred from the brass shot to the water using Q = mcΔT. We know that the mass of the brass shot is 50 grams and the specific heat capacity of brass is 0.38 J/g°C. The initial temperature of the brass shot is 200°C and the final temperature will be the equilibrium temperature. Therefore, we can write the equation as:

Q = (50 g) (0.38 J/g°C) (200°C - T)

Next, we can calculate the heat transferred from the water to the brass shot using the same equation. The mass of the water is 160 grams and the specific heat capacity of water is 4.18 J/g°C. The initial temperature of the water is 20°C and the final temperature will also be the equilibrium temperature. Therefore, we can write the equation as:

Q = (160 g) (4.18 J/g°C) (T - 20°C)

Since the heat transferred from the brass shot to the water is equal to the heat transferred from the water to the brass shot, we can set these two equations equal to each other and solve for T:

(50 g) (0.38 J/g°C) (200°C - T) = (160 g) (4.18 J/g°C) (T - 20°C)

After solving for T, we get the equilibrium temperature to be approximately 59.4°C. This means that after the brass shot is dropped into the water, both the brass shot and the water will reach a final temperature of 59.4°C.

In summary, to solve this thermal equilibrium problem, we used the equation Q = mcΔT and set the heat transferred from the brass shot to the water equal to the heat transferred from the water to the brass shot. From there, we were able to solve for the equilibrium temperature.