A 30 ounce iron bar at 425 degrees Fahrenheit is placed in 2.00 quarts of water at 80.0 degrees Fahrenheit. What will be the change in temperature of the iron bar in degrees Fahrenheit?
(Assume 1/3 heat lost to the surroundings)
Specific heat of iron= .473 Joules/grams degrees Celcius.
q(loss of Fe) = - q(gain of water)
q= m*specific heat * delta T(which is Tf-Ti)
Note: convert your units first.
To find the change in temperature of the iron bar, we can use the principle of heat transfer. The heat lost by the iron bar is equal to the heat gained by the water, neglecting the heat lost to the surroundings.
First, let's convert the units to a consistent system. We'll convert the temperature to degrees Celsius, the mass of the iron bar to grams, and the specific heat of iron to joules/grams degrees Celsius.
Given:
- Mass of the iron bar: 30 ounces
- Initial temperature of the iron bar: 425 degrees Fahrenheit
- Volume of water: 2.00 quarts
- Initial temperature of water: 80.0 degrees Fahrenheit
- Specific heat of iron: 0.473 joules/grams degrees Celsius
1. Convert the mass of the iron bar to grams:
- Since 1 ounce is approximately equal to 28.35 grams, the mass of the iron bar in grams is:
mass_iron = 30 ounces * 28.35 grams/ounce
2. Convert the temperatures to degrees Celsius:
- Use the conversion formula:
T_Celsius = (T_Fahrenheit - 32) * 5/9
where T_Celsius is the temperature in degrees Celsius, and T_Fahrenheit is the temperature in degrees Fahrenheit.
- Convert the initial temperature of the iron bar:
initial_temp_iron_Celsius = (425 - 32) * 5/9
- Convert the initial temperature of the water:
initial_temp_water_Celsius = (80 - 32) * 5/9
3. Calculate the heat lost by the iron bar using the formula:
heat_lost_iron = mass_iron * specific_heat_iron * (initial_temp_iron_Celsius - final_temp_iron_Celsius)
- Since we want to find the change in temperature, the final temperature of the iron bar is unknown. We'll call it final_temp_iron_Celsius.
4. Calculate the heat gained by the water using the formula:
heat_gained_water = mass_water * specific_heat_water * (final_temp_water_Celsius - initial_temp_water_Celsius)
- Since we know the initial temperature of the water (80.0 degrees Fahrenheit) and the volume of water (2.00 quarts), we need to determine the mass of water and the specific heat of water.
- The specific heat of water is approximately 1 calorie/gram degrees Celsius, which is equivalent to 4.18 joules/gram degrees Celsius.
- Given that 1 quart is approximately equal to 946.3529 grams, the mass of the water in grams is:
mass_water = 2.00 quarts * 946.3529 grams/quart
5. Equate the heat lost by the iron bar to the heat gained by the water to find the final temperature of the iron bar:
heat_lost_iron = heat_gained_water
- Substitute the values and solve for final_temp_iron_Celsius.
6. Convert the final temperature of the iron bar from degrees Celsius to degrees Fahrenheit:
final_temp_iron_Fahrenheit = final_temp_iron_Celsius * 9/5 + 32
The change in temperature of the iron bar in degrees Fahrenheit is the difference between the initial temperature and the final temperature of the iron bar, final_temp_iron_Fahrenheit - initial_temp_iron_Fahrenheit.
By following these steps and performing the necessary calculations, you can determine the change in temperature of the iron bar.