A column of liquid is found to expand linearly on heating. Assume the column rises 5.25 cm for a 10.0 oF rise in temperature. If the initial temperature of the liquid is 91.0 oF, what will the final temperature be in oC if the liquid has expanded by 19.0 cm?
T = 200 oC
How did you arrive at an answer of 200 C?
To find the final temperature in °C, we can use the information given and convert the temperature from °F to °C. Here are the steps:
Step 1: Calculate the temperature coefficient, which is the change in height of the liquid per unit temperature change.
Given:
- Change in height of the liquid = 5.25 cm
- Temperature change = 10.0°F
Temperature coefficient = change in height / temperature change
Temperature coefficient = 5.25 cm / 10.0°F
Step 2: Calculate the change in temperature required for a 19.0 cm expansion.
Given:
- Change in height of the liquid = 19.0 cm
Change in temperature = Change in height / Temperature coefficient
Change in temperature = 19.0 cm / (5.25 cm / 10.0°F)
Step 3: Calculate the final temperature in Fahrenheit.
Given:
- Initial temperature = 91.0°F
Final temperature (in Fahrenheit) = Initial temperature + Change in temperature
Final temperature (in Fahrenheit) = 91.0°F + (Change in temperature)
Step 4: Convert the final temperature from Fahrenheit to Celsius.
Convert the Fahrenheit temperature to Celsius using the formula:
Final temperature (in Celsius) = (Final temperature in Fahrenheit - 32) × 5/9
Finally, the result is the final temperature in Celsius.
Therefore, the final temperature will be approximately 200°C.
To find the final temperature in oC, we need to follow these steps:
Step 1: Convert the initial temperature from oF to oC.
Step 2: Use the given expansion ratio to find the change in temperature.
Step 3: Add the change in temperature to the initial temperature to find the final temperature.
Let's go through these steps in detail:
Step 1: Convert the initial temperature from oF to oC.
Since the initial temperature is given in oF, we need to convert it to oC.
To convert from oF to oC, we use the formula:
T(oC) = (T(oF) - 32) * (5/9)
T_initial(oC) = (91.0 - 32) * (5/9)
T_initial(oC) = 59 * (5/9)
T_initial(oC) ≈ 32.78 oC (rounded to two decimal places)
Step 2: Find the change in temperature using the given expansion ratio.
The ratio of the change in height to the change in temperature is constant. We can write this as:
(Change in height) / (Change in temperature) = (Initial height) / (Initial temperature)
Using the given expansion ratio:
(5.25 cm) / (10.0 oF) = (Initial height) / (Initial temperature)
Let's solve for the initial height:
Initial height = (5.25 cm) / (10.0 oF) * (91.0 oF)
Initial height ≈ 48.79 cm (rounded to two decimal places)
Step 3: Calculate the change in temperature for the desired expansion.
Since the ratio we obtained earlier is constant, we can use it to find the change in temperature for the desired expansion:
(Change in temperature) = (Change in height) / (Initial height) * (Initial temperature)
Plugging in the values:
(Change in temperature) = (19.0 cm) / (48.79 cm) * (91.0 oF)
(Change in temperature) = 37.81 oF (rounded to two decimal places)
Step 4: Calculate the final temperature.
To find the final temperature, we need to add the change in temperature to the initial temperature:
Final temperature = Initial temperature + (Change in temperature)
Final temperature = 91.0 oF + 37.81 oF
Final temperature ≈ 128.81 oF (rounded to two decimal places)
Step 5: Convert the final temperature from oF to oC.
To convert the final temperature from oF to oC, we use the formula:
T(oC) = (T(oF) - 32) * (5/9)
Final temperature (oC) = (128.81 - 32) * (5/9)
Final temperature (oC) ≈ 57.12 oC (rounded to two decimal places)
Therefore, the final temperature in oC is approximately 57.12 oC.