Metal in water thermal equilibrium? Help

In summary: Guy puts a copper bar with a mass of 5.0 kg in the oven and puts an identical bar in a well-insulated 20.0 liter vessel containing 5.00 L of liquid water and the rest saturated steam at 760 mmHg. Waits until bars reach thermal equilibrium with their surroundings, then quickly takes the first bar out of the oven, removes the second bar from the vessel, drops the first bar in its place, covers the vessel tightly, waits for the system to come to equilibrium, and records the pressure gauge reading inside the vessel. It is 50.1 mmHg. The specific gravity of copper is 8.92. The internal energy of copper is given by U hat (kJ
  • #1
madbeemer
12
0
Metal in water thermal equilibrium?? Help

Determining temperature of an oven.

Guy puts a copper bar with a mass of 5.0 kg in the oven and puts an identical bar in a well-insulated 20.0 liter vessel containing 5.00 L of liquid water and the rest saturated steam at 760 mmHg. Waits until bars reach thermal equilibrium with their surroundings, then quickly takes the first bar out of the oven, removes the second bar from the vessel, drops the first bar in its place, covers the vessel tightly, waits for the system to come to equilibrium, and records the pressure gauge reading inside the vessel. It is 50.1 mmHg. Specific gravity of copper is 8.92. Specific internal energy of copper is given by U hat (kJ/kg) = 0.36*T(degrees celcius). to calculate oven temperature.

a) assume bar can transfer from oven to vessel without losing heat. What temperature is the oven? How many grams H2O evaporate?
b) bar actually lost 8.3 kJ of heat b/w oven and the vessel. Whatis the true oven temperature.
 
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  • #2
Anyone have an idea? We worked on this shet for 3 hours, but couldn't relate the information and pressure stuff. Involves energy equil. and stuff.
 
  • #3
The fact that the bars are identical removes the volume from consideration of the change in pressure in the vessels, so any change in pressure is due to thermal effects (heat transfer) from the block.

There is some energy content in the heated bar, which is related to the mass, specific heat and temperature of the bar.

Then there is the initial conditions in the vessel, water and sat steam at 760 mm Hg, which is 1 atm (I expect absolute pressure by the wording) so the temperature of the water must be 100°C. Now the gage reading (usually gage pressure) is 50.1 mm Hg, which is equiavlent to 760+50.1 mmHg absolute. So there is a differential pressure of 50.1 mmHg, which comes from the heat.

The heat is transferred from the block to the water - and some of the 5.0 l of water is converted to steam - hence the rise in pressure. There is heat of vaporization involved. There is change of phase in a constant volume (20 l) process.

We know that that the heated block must have a temperature greater than

Heat content (thermal energy) = m cp(T) or
Change in heat content = m cp([itex]\Delta[/itex]T)

See also - http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/spht.html
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/heat.html
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/inteng.html
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/intengcon.html
 

1. What is thermal equilibrium?

Thermal equilibrium is the state in which two objects or substances are at the same temperature and there is no transfer of heat between them.

2. How does metal affect thermal equilibrium in water?

Metal has a high thermal conductivity, meaning it can transfer heat quickly. When metal is placed in water, it can absorb or release heat, causing the water to reach thermal equilibrium with the metal.

3. Can metal in water reach thermal equilibrium with the surrounding air?

Yes, if the metal and water are in an open system, they can reach thermal equilibrium with the surrounding air. This is because air is also a fluid and can transfer heat to and from the water and metal.

4. How does the amount of metal affect thermal equilibrium in water?

The amount of metal in water can affect thermal equilibrium by changing the rate at which heat is transferred. A larger amount of metal will have a greater surface area and can transfer heat more quickly, while a smaller amount of metal will take longer to reach thermal equilibrium with the water.

5. What factors can affect thermal equilibrium between metal and water?

Some factors that can affect thermal equilibrium between metal and water include the type of metal, the temperature of the water and metal, the surface area of the metal, and the presence of any insulating materials. These factors can impact the rate at which heat is transferred and the final temperature reached by the metal and water.

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