An ungraduated mercury thermometer attached to a millimeter scale read 22.8mm in ice and 242mm in steam at standard pressure. what will the millimeter read when the temperature is 20?
To determine the millimeter reading on the ungraduated mercury thermometer at a temperature of 20 degrees Celsius, we need to use the information provided about the readings in ice and steam.
The first step is to establish a linear relationship between the temperature and the millimeter reading on the thermometer. We can do this by finding the slope of the line that connects the ice and steam points.
Given:
- Reading in ice = 22.8 mm
- Reading in steam = 242 mm
Next, we need to find the temperature at which the mercury thermometer reads 0 mm. This will be our reference point or "zero" on the scale. Since the thermometer is ungraduated, we can't directly determine the value, but it is an important reference for calculating the readings at other temperatures.
Once we have the temperature at which the thermometer reads 0 mm, we can use the slope of the line to determine the millimeter reading at a temperature of 20 degrees Celsius.
Here's a step-by-step breakdown:
Step 1: Determine the slope of the line
To find the slope, we use the formula:
slope = (y2 - y1) / (x2 - x1)
Where:
- x1 is the temperature in ice,
- y1 is the reading in ice,
- x2 is the temperature in steam,
- y2 is the reading in steam.
Using the given values:
- x1 = temperature in ice = 0 degrees Celsius
- y1 = reading in ice = 22.8 mm
- x2 = temperature in steam = 100 degrees Celsius (at standard pressure)
- y2 = reading in steam = 242 mm
Substituting the values into the formula:
slope = (242 - 22.8) / (100 - 0)
slope = 219.2 / 100
slope = 2.192
Step 2: Find the temperature at which the thermometer reads 0 mm
Since the thermometer is ungraduated, we need to determine the temperature at which the mercury level reaches 0 mm.
To do this, we can use the slope we calculated in the previous step:
0 = 2.192 * temperature + b
Solving for 'temperature' gives us:
temperature = -b / 2.192
We need to find the value of 'b' to calculate the temperature. To do this, we use one of the known data points. Let's use the ice point, which is at 0 degrees Celsius:
0 = 2.192 * 0 + b
b = 0
Therefore, the temperature at which the thermometer reads 0 mm is 0 degrees Celsius.
Step 3: Determine the millimeter reading at 20 degrees Celsius
Now that we have determined the temperature at which the thermometer reads 0 mm, we can use the slope to find the reading at 20 degrees Celsius.
Using the formula:
reading = slope * temperature + b
Substituting the values:
slope = 2.192
temperature = 20 degrees Celsius
b = 0
reading = 2.192 * 20 + 0
reading ≈ 43.84 mm
Therefore, the millimeter reading on the ungraduated mercury thermometer at a temperature of 20 degrees Celsius would be approximately 43.84 mm.