Thermodynamics:
Problem-Solving Example
Problem-Solving Page
In this module:
Problem 1
Problem 2
Problem 3

Now, calculate how much water is needed to absorb that much heat. Assume that the water enters the plant at 25 ºC and heat pollution rules prohibit the discharge of water warmer than 30 ºC. Express your answer in gallons of water per kilogram of phosphorus.

1 g H2O=1 mL H2O
1 L=1.056710 qt
4 qt=1 gal
c (H2O (l))=4.184 J/g ºC

Step1: Identify the system and surroundings.

Step 2: Identify and assign signs to all the kinds of energy and work entering or leaving the system.

Step 3: Predict the units your answer should have.

Step 4: Predict the approximate magnitude of your answer.

Answer:


Correct! Nearly 8 gallons of water are needed to condense about 2 pounds of phosphorus. A major phosphoric acid plant could conceivably produce a ton of phosphorus in a day, which would require 8000 gallons of water. Can you see why many factories are located near a river for a source of cool water? Click on the Next button below to return to the Problem-Solving Page or on the Close button to close this window.

    

See the calculation below. Nearly 8 gallons of water are needed to condense about 2 pounds of phosphorus. A major phosphoric acid plant could conceivably produce a ton of phosphorus in a day, which would require 8000 gallons of water. Can you see why many factories are located near a river for a source of cool water? Click on the Next button below to return to the Problem-Solving Page or on the Close button to close this window.

q=m c DT ==> m=q / c • DT
m=598 kJ/kg phosphorus / (4.184 J/gºC • (30 - 25) ºC) • 1000 J/kJ • 1 mL H2O/1g H2O • 1 L/1000 mL • 1.056710 qt/L • 1 gal/4qt
m=7.55 gal H2O / kg phosphorus

    

While numerically correct, your answer has the wrong number of significant digits. Try again.
Remember to include units with your answer.

Your answer has the wrong sign. In this case, the water's temperature is rising, so the heat it gains has a positive sign. Does it make sense that a negative volume of water is needed to cool the phosphorus? You may not have changed the sign of the heat from the previous problem, or you may have confused the initial and final temperatures of the water.

That is incorrect. Try again.
Remember, this problem doesn't call for the calculation of an amount of energy.