15g iron (c=450 J/kg K) bolt is heated from 21 C to 312 C. It is then plunged into a 2kg of 15 C water (c= 4180 J/kg K) into a 4.6kg alum. tub (c=903 J/kg K) What is the final temp. (Tf) of the water and the tub?

for some reason..., i got 0.472 C for final temp of tub and -14.765 C for temp of water.....

i don't understand this question, plz help.

At final equilibrium, the temperatures of water, iron and tub must be equal. Assume the heat energy lost by the iron equals the heat gained by the tub and water.

You must have made some serious errors in setting up the problem. You have the water freezing by adding the heated iron.

The starting temperature of 21 C before the iron is heated makes no differense in the answer. It is what happens after it reaches 312 C and is cooled that matters.

To solve this problem, we need to use the principle of conservation of energy. The heat gained by the water and the tub is equal to the heat lost by the iron bolt.

First, let's calculate the heat gained by the water and the tub.

The initial temperature of the water is 15°C, the final temperature is the unknown (Tf), and the heat capacity of the water is 4180 J/kg K. The mass of the water is 2 kg.

Q1 = (mass)(specific heat capacity)(change in temperature)
Q1 = (2 kg)(4180 J/kg K)(Tf - 15)

Next, let's calculate the heat gained by the tub.

The initial temperature of the tub is also 15°C, the final temperature is the unknown (Tf), and the heat capacity of the tub is 903 J/kg K. The mass of the tub is 4.6 kg.

Q2 = (mass)(specific heat capacity)(change in temperature)
Q2 = (4.6 kg)(903 J/kg K)(Tf - 15)

Now, let's calculate the heat lost by the iron bolt.

The initial temperature of the iron bolt is 21°C, and the final temperature is 312°C. The mass of the iron bolt is 15 g, which is equal to 0.015 kg. The heat capacity of iron is 450 J/kg K.

Q3 = (mass)(specific heat capacity)(change in temperature)
Q3 = (0.015 kg)(450 J/kg K)(312 - 21)

According to the principle of conservation of energy, the heat gained by the water and the tub (Q1 + Q2) is equal to the heat lost by the iron bolt (Q3).

Q1 + Q2 = Q3

((2 kg)(4180 J/kg K)(Tf - 15)) + ((4.6 kg)(903 J/kg K)(Tf - 15)) = (0.015 kg)(450 J/kg K)(312 - 21)

Now, you can solve this equation to find the final temperature (Tf) of the water and the tub.