# What is the equilibrium temperature of copper and water?

• Altairs
In summary, the conversation discusses the process of finding the equilibrium temperature between a 50 Kg block of copper at 80C and 120L of water at 25C. Specific heat values for water and copper are used, but the calculated answer is below 25C instead of being between 25 and 80. The importance of showing working and using the total heat change equation is emphasized.

#### Altairs

I am not a novice at thermodynamics but still the following question made me think over my status more than twice.

I have to find the equilibrium temperature when a 50 Kg block of copper at 80C is placed in a container which as 120L of water at 25C.

I made simple equations of heat lost = heat gained. Used Specific Heat for water = 4.18 and for copper 0.285 (and 0.391) and used mcdelT. But the answer I get is below 25C. Where as it should be between 25 and 80.

Altairs said:
I made simple equations of heat lost = heat gained. Used Specific Heat for water = 4.18 and for copper 0.285 (and 0.391) and used mcdelT. But the answer I get is below 25C. Where as it should be between 25 and 80.

Hi Altairs!

You know you should show us your working … otherwise how can we see where you went wrong?

Oh I forgot the PF SOP

Heat Lost (by copper) = Heat Gained (by water)

$$50 * 0.385 (T_{e} - 80) = 0.12 * 1000 *4.18 (T_{e} - 25)$$

Altairs said:
Oh I forgot the PF SOP

Heat Lost (by copper) = Heat Gained (by water)

$$50 * 0.385 (T_{e} - 80) = 0.12 * 1000 *4.18 (T_{e} - 25)$$

no wonder they both got colder!

It would be less confusing if you said "total heat change = 0, therefore:"

$$50 * 0.385 (T_{e} - 80)\,+\,0.12 * 1000 *4.18 (T_{e} - 25)\,=\,0$$

Ooh ! Thanks

## 1. What is equilibrium temperature?

Equilibrium temperature is the state at which the rate of energy absorbed by an object is equal to the rate of energy emitted by that object, resulting in a constant temperature.

## 2. How is equilibrium temperature calculated?

Equilibrium temperature can be calculated using the Stefan-Boltzmann law, which states that the rate of energy emitted by an object is proportional to the fourth power of its temperature.

## 3. What factors affect equilibrium temperature?

The factors that affect equilibrium temperature include the intensity of incoming radiation, the albedo (reflectivity) of the object's surface, and the object's specific heat capacity.

## 4. Why is equilibrium temperature important?

Equilibrium temperature is important because it helps us understand the energy balance of objects in space and on Earth, and provides insight into the behavior of the Earth's climate system.

## 5. Is equilibrium temperature the same for all objects?

No, equilibrium temperature varies depending on the specific characteristics of an object, such as its size, shape, composition, and distance from its energy source.