A mercury in glass thermometer reads 4cm at ice point and 29cm at steam point. Calculate the temperature when the mercury level is at 9cm
13°C
Calculate the temperature when the mecurylevel is 9cm
20
To calculate the temperature when the mercury level is at 9cm, we need to use the concept of linear interpolation. Linear interpolation is a method of estimating a value between two known values based on their relative positions.
First, we need to determine the difference between the two known values (the ice point and steam point) on the thermometer. In this case, the difference is 29cm - 4cm = 25cm.
Next, we need to determine the fraction of the difference that corresponds to the 9cm mark. This fraction can be calculated by dividing the difference between the desired mercury level and the lower known value by the total difference.
Fraction = (9cm - 4cm) / (29cm - 4cm) = 5cm / 25cm = 1/5
Now that we have the fraction, we need to determine the temperature difference between the ice point and steam point. In most mercury thermometers, this difference is usually divided into equal divisions, meaning each division corresponds to the same temperature increment.
Let's assume that the difference in temperature between the ice point and steam point is divided into 100 equal divisions. Therefore, each division corresponds to a temperature increment of (steam point temperature - ice point temperature) / 100.
Temperature increment = (29°C - 0°C) / 100 = 0.29°C
Finally, to calculate the temperature when the mercury level is at 9cm, we multiply the fraction by the total number of temperature increments and add it to the temperature at the lower known value.
Temperature = (1/5) * (100 * 0.29°C) + 0°C
Temperature = 20 * 0.29°C + 0°C
Temperature = 5.8°C + 0°C
Temperature = 5.8°C
Therefore, when the mercury level is at 9cm, the temperature is approximately 5.8°C.