How much water is needed to cool a block of aluminum to a specific temperature?

In summary, the question asks for the mass of water needed to reach thermal equilibrium with a 1.85kg cube of aluminum initially at 150 degrees C to lower the temperature of the aluminum to 65 degrees C. Using the equation Q = ΔT * m * C, with ΔT as the temperature difference, m as the mass, and C as the specific heat, the correct answer is .845kg. The concept of thermal equilibrium means that the water and aluminum reach the same final temperature as heat is transferred between them. The specific heat and temperature units do not need to be converted as the difference in temperature is the same in both degrees C and K.
  • #1
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Homework Statement


What mass of water at 25dC (d = degrees) must be allowed to come to thermal equalibrium with a 1.85kg cube of aluminum initially at 1.5*10*2dC to lower the temperature of the aluminum to 65dC? Assume the water doesn't turn to steam.


Homework Equations


Q = Del(T)m(C), DelT= change in temperature, m = mass, C = specific heat. It doesn't actually give any equation I just assume that it deals with that one.


The Attempt at a Solution


(after conversion to Kelvin)

85K * (1.85kg) * (.91kJ/(kgK)aluminum = 143.0975kJ

143.0975kJ = 125K * m * (4.18kJ/kgK)water

I assumed this was the amount energy involved in the temperature change from aluminum at 423K to 338K, and assumed the energy is conserved since conservation of energy was a topic recently and so assumed the amount of energy that the aluminum cooled by the was amount of energy the water gained. It makes sense at first me at first except I don't understand exactly how to consider the "equilibrium" part of it, I know from calculus there's Newton's law of Cooling and so I don't know why/how that's used with varying temperatures and masses to cool something to an equilibrium instead, and neither do I get exactly how an equilibrium is being considered in this situation. Anyway, it said the answer was .845kg and I got .273kg.
 
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  • #2
Why does everyone get their question answered but me :(
 
  • #3
The final temperature for the water will equal the final temperature for the aluminum, they're in thermal equilibrium.

You listed change in temperature for water as going from initial to aluminums initial, 150. Sub in delta T to be 40 instead of 125.
 
  • #4
'Thermal equilibrium' means the water and the aluminum have reached the same temperature. As heat is transferred from the aluminum cube to the water, the metal cools while the water heats up.

You aren't being asked how long this process takes, so Newton's Law of Cooling isn't useful for this problem.

Although specific heats are given in units of kJ/K-kg and temperatures are given in degrees C, you don't need to convert temperature from degrees C to degrees K because you are interested in the amount of heat it takes to change the temperature of a substance, and a temperature difference of 1 degree C is the same temperature difference of 1 degree K.

It's not clear why you said the temperature of the water would increase by 125 degrees K. After all, since the water had an initial temperature of 25 C, an increase of 75 C would bring the water to its boiling point of 100 C. That's why your mass calculation failed.
 
  • #5
I didn't get the exact number but I got pretty close, thanks.
 

FAQ: How much water is needed to cool a block of aluminum to a specific temperature?

1. What is heat transfer?

Heat transfer is the movement of thermal energy from one object or system to another due to a difference in temperature. This can occur through three main mechanisms: conduction, convection, and radiation.

2. What is a heat transfer problem?

A heat transfer problem refers to a specific scenario where there is a need to analyze and understand how heat is being transferred between objects or systems. This could involve determining the rate of heat transfer, the direction of heat flow, or the temperature distribution within the system.

3. What are the factors that affect heat transfer?

The rate of heat transfer is influenced by several factors, including the temperature difference between the objects, the thermal conductivity of the materials, the surface area and distance between the objects, and the presence of any insulating materials.

4. How is heat transfer measured?

The rate of heat transfer is typically measured in units of watts (W) or joules per second (J/s). The amount of heat transferred can also be measured in units of joules (J) or calories (cal). These measurements can be obtained through experiments or calculated using mathematical equations.

5. What are some real-life examples of heat transfer problems?

Examples of heat transfer problems can be found in various fields, such as engineering, physics, and environmental science. Some common examples include determining the rate of heat loss in a building, analyzing the cooling of electronic devices, and studying the transfer of heat in the Earth's atmosphere.

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