# Thermal Equilibrium of Hot Iron & Water

• TT0
In summary, a hot iron nail with a mass of 150 g and a temperature of 800 K is placed in 1.0 kg of water with a temperature of 25°C. Using the equation Q=mc∆T, we can find the common temperature of the two objects once they reach thermal equilibrium by setting Q lost in the nail equal to Q gained in the water. After solving for the final temperature, we get a value of -280.38 K, which is negative. However, after correcting for a mistake in the equation, the final temperature is found to be 33.06°C, which is a reasonable result.
TT0

## Homework Statement

A hot (800 K) iron nail of mass 150 g is placed into a 1.0 kg of water at 25°C. What is the common temperature of the 2 objects once they have reached thermal equilibrium? Assume no change of state of the water.

Heat capacity of iron nail is 450 J/kg/K
Heat capacity of water is 4138 J/kg/K

Q=mc∆T

## The Attempt at a Solution

Q lost in nail=Q gained in water

let T = final temperature

0.15*450*(800-T)=1*4138*(T+25+273)
T=-280.38 K

I don't know why it is negative. Can someone explain what I did wrong?

(T+25+273) should be a difference between the final temperature and initial temp.

TT0
I see thanks!

Seems reasonable

TT0
Thanks again!

## 1. What is thermal equilibrium?

Thermal equilibrium is a state in which two objects or substances at different temperatures reach a balance, resulting in a constant temperature throughout the system.

## 2. How does hot iron and water reach thermal equilibrium?

When hot iron is placed in water, the energy from the iron is transferred to the water through conduction. This process continues until the temperatures of the iron and water are equal and thermal equilibrium is reached.

## 3. What factors can affect the thermal equilibrium of hot iron and water?

The rate at which thermal equilibrium is reached can be affected by the initial temperatures of the iron and water, the heat capacity of the substances, and the surface area of the objects in contact.

## 4. Can thermal equilibrium be achieved in an isolated system?

Yes, thermal equilibrium can be achieved in an isolated system as long as there are no external sources of heat or energy. In this case, the system will reach a state of constant temperature.

## 5. Why is thermal equilibrium important in scientific experiments?

Thermal equilibrium is important in scientific experiments because it allows for accurate and consistent results. Without reaching thermal equilibrium, the temperatures of the substances being studied can continue to change, making it difficult to draw meaningful conclusions.

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