Thermodyanmics, specific heat capacity

[Jennifer001]

Homework Statement

a 4kg iron hammer is initally 700 degree celcius is droppped into a bucket containing 20kg of water at 25degree celcius. what is the final temperture

Homework Equations

q=mc(delta)T

The Attempt at a Solution

m1=4kg
m2=20kg
T1=700=973K
T2=25=298
i know the system is in equilibrium but i don't know how to solve it correctly.. so here's my shot at it

Q=mc(delta)T
=(4)(449J/kgK)(Tf-973)=(20)(4190J/kgK)(Tf-298)

i think I'm doing this question wrong because .. when i solve for Tf i get a negative number of -288.66K

help?

 

[Jennifer001]

nvm forget this question i just figured out how to do it... i forgot to put the negative sign for the iron since it loses heat.

 

[thomate1]

As a scientist, it is important to note that the equation used to solve this problem is correct. However, the final temperature calculated is not physically possible. This is because the hammer is initially at a much higher temperature than the water, and when they come into contact, heat will transfer from the hammer to the water until they reach thermal equilibrium. This means that the final temperature should be somewhere in between the initial temperatures of the hammer and the water.

To solve this problem correctly, we need to use the law of energy conservation, which states that the total energy of a closed system remains constant. In this case, the total energy is the sum of the heat energy of the hammer and the water.

We can set up the following equation:

m1c1(T1-Tf) = m2c2(Tf-T2)

Where m1 and c1 are the mass and specific heat capacity of the hammer, T1 is the initial temperature of the hammer, m2 and c2 are the mass and specific heat capacity of the water, and T2 is the initial temperature of the water.

Solving for Tf, we get:

Tf = (m1c1T1 + m2c2T2)/(m1c1 + m2c2)

Plugging in the values, we get:

Tf = (4kg * 449J/kgK * 700K + 20kg * 4190J/kgK * 25K) / (4kg * 449J/kgK + 20kg * 4190J/kgK) = 25.1 degrees Celsius

Therefore, the final temperature will be approximately 25.1 degrees Celsius, which is a more reasonable result.