Temperature & Heat: Equilibrium of 1 kg Aluminium & Water

In summary: C and 10 degrees C, since heat will transfer from the aluminum to the water until they reach equilibrium. In summary, to determine the temperature when the aluminum and water reach equilibrium, you will need to set up two equations using the specific heat capacities of aluminum and water, and solve for the two unknown delta T values. This will give you the final temperature at equilibrium.
  • #1
superdave
150
3
A .1 kg piece of aluminum at 90 degrees C is submerged in 1 KG of water at 10 degrees C. What is the temperature when they reach equalibrium?

Now I know, aluminum has a c of 920 J/(kg * degree C) and water has a c of 4186 J/(kg * degree C).

I'm not sure how to approach this.

Best I can think of is setting m*c*dT for the water equal to m*c*dT for the aluminum. But I have two unknown variables there. (The dT's) So that can't be right. Help is appreciated.
 
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  • #2
What is the definition for your delta T? It is [tex]\Delta T = T_{end} - T_{start}[/tex]

Does that point you in the right direction? Also, think about the physical situation when the two have reached equillibrium...
 
  • #3
superdave said:
A .1 kg piece of aluminum at 90 degrees C is submerged in 1 KG of water at 10 degrees C. What is the temperature when they reach equalibrium?

Now I know, aluminum has a c of 920 J/(kg * degree C) and water has a c of 4186 J/(kg * degree C).

I'm not sure how to approach this.

Best I can think of is setting m*c*dT for the water equal to m*c*dT for the aluminum. But I have two unknown variables there. (The dT's) So that can't be right. Help is appreciated.
This means you will need to work out two equations to determine the values of these two different delta T's.

AM
 

FAQ: Temperature & Heat: Equilibrium of 1 kg Aluminium & Water

1. What is the specific heat capacity of aluminium and water?

The specific heat capacity of aluminium is 0.897 J/g°C and the specific heat capacity of water is 4.186 J/g°C. This means that it takes 0.897 joules of energy to raise the temperature of 1 gram of aluminium by 1 degree Celsius, and 4.186 joules of energy to raise the temperature of 1 gram of water by 1 degree Celsius.

2. How does temperature affect the equilibrium between aluminium and water?

Temperature affects the equilibrium between aluminium and water by changing the rate of heat transfer between the two materials. When the temperature of aluminium is higher than that of water, heat will flow from the aluminium to the water until they reach equilibrium. Similarly, when the temperature of water is higher, heat will flow from the water to the aluminium.

3. What is the equilibrium temperature of 1 kg of aluminium and water?

The equilibrium temperature of 1 kg of aluminium and water will depend on the initial temperatures of the two materials. However, assuming that both materials are initially at room temperature (around 25°C), the equilibrium temperature will be around 25°C as well. This is because the specific heat capacity of water is higher than that of aluminium, meaning that water can absorb more heat energy before reaching the same temperature as aluminium.

4. How do we calculate the amount of heat transferred between aluminium and water at equilibrium?

The amount of heat transferred between aluminium and water at equilibrium can be calculated using the equation Q = mCΔT, where Q is the amount of heat transferred, m is the mass of the material, C is the specific heat capacity, and ΔT is the change in temperature. In this case, we would use the specific heat capacities of aluminium and water to calculate the amount of heat transferred between the two materials at equilibrium.

5. How does the equilibrium between aluminium and water change if the amount of each material is increased?

If the amount of aluminium and water is increased, the equilibrium temperature will remain the same, but more heat will be transferred between the two materials to reach equilibrium. This is because there is a larger mass of each material, so more heat energy is required to raise the temperature of each material by 1 degree Celsius. The equilibrium will still be reached when the temperatures of both materials are equal.

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