Final Temp of Water & Zinc: Find the Answer

[DrMcDreamy]

Homework Statement

A 10 kg piece of zinc at 68◦C is placed in a container of water. The water had a mass of 32 kg and a temperature of 14◦C before the zinc was added. The specific heat of zinc and water are 388 J/kg ·◦C and 4180 J/kg ·◦C. What is the final temperature of water and zinc? Answer in units of ◦ C.

Homework Equations

How do you do this? What formula do I use? TIA

 

[danago]

Think about the law of energy conservation. If you assume that the system is insulated from the surroundings, then any heat transferred from the water will be absorbed by the zinc. i.e.:

Energy gained by water = energy lost by zinc

You also know that two objects in contact will eventually reach thermal equilibrium, so that their final temperatures are the same. What final temperature, T, will make the energy transferred by the water and zinc equal?

 

[DrMcDreamy]

So is it 41 C?

 

[DrMcDreamy]

m_ZnC_Zn(T_f-T_{Zn i}) + m_H2OC_H2O(T_f-T_{H2O i})=0

When I plug in my numbers:

(10 kg)(388 J/kg C)(T_f-68 C) + (32 kg)(4180 J/kg C)(T_f- 14 C) = 0
3880 J/C (T_f-68 C) + 133760 J/C (T_f- 14 C) = 0

Than?!

 

[rwisz]

To find the final temperature of the water and zinc, you can use the formula Q = mCΔT, where Q is the heat transferred, m is the mass, C is the specific heat, and ΔT is the change in temperature. In this case, you will have two equations, one for the zinc and one for the water, and you can solve for the final temperature of each substance.

For the zinc:
Q = (10 kg)(388 J/kg·°C)(Tf - 68°C)
For the water:
Q = (32 kg)(4180 J/kg·°C)(Tf - 14°C)

Since the heat transferred is the same for both substances, you can set the two equations equal to each other and solve for Tf, the final temperature:

(10 kg)(388 J/kg·°C)(Tf - 68°C) = (32 kg)(4180 J/kg·°C)(Tf - 14°C)

After solving, you will find that the final temperature of the water and zinc is 16.57°C.

Please note that this is a simplified calculation and does not take into account any heat loss to the surroundings or changes in density of the water. It is always important to consider all factors and assumptions when solving a problem in science.