The ice point of a faulty mercury in glass thermometer isX degree celcius while its steam point is 85 degree celcius. If the thermometer reads 50 degree celcius when the true temperature is 40 degree celcius, calculate the value of X

To calculate the value of X, we need to use the concept of linear interpolation.

Linear interpolation is a method of estimating a value between two known data points on a straight line. In this case, the known data points are the ice point and steam point of the faulty mercury thermometer.

Let's denote the ice point as X and the steam point as 85 degrees Celsius.

Given:
True temperature = 40 degrees Celsius
Thermometer reading = 50 degrees Celsius

Using linear interpolation, we can find the value of X. The formula for linear interpolation is:

X = ((y - y1)/(y2 - y1)) * (x2 - x1) + x1

Where:
X = Unknown value (ice point)
x1 = Reading at the ice point (Unknown temperature)
x2 = Reading at the steam point (85 degrees Celsius)
y1 = True temperature at the ice point (Unknown temperature)
y2 = True temperature at the steam point (85 degrees Celsius)
y = Given true temperature (40 degrees Celsius)

Plugging in the values into the equation:

X = ((40 - Y1)/(Y2 - Y1)) * (X2 - X1) + X1

X = ((40 - X)/(85 - X)) * (85 - X) + X

Simplifying the equation:

X = (40 - X) + X

X = 40

Therefore, the value of X, which represents the ice point of the faulty thermometer, is 40 degrees Celsius.

To calculate the value of X, which represents the ice point of the faulty thermometer, we need to use the concept of calibration.

First, let's understand what calibration means in this context. Calibration is the process of determining the accuracy of a measuring instrument and correcting any inherent errors. In the case of a faulty thermometer, we need to account for its inaccurate readings by calibrating it based on known reference points.

Here, we know that the true temperature is 40 degrees Celsius when the thermometer reads 50 degrees Celsius. This means the faulty thermometer is consistently measuring 10 degrees Celsius higher than the actual temperature.

To find the value of X, we need to consider the temperature difference between the ice point and the true temperature. According to the given information, the steam point is at 85 degrees Celsius. The ice point will be lower than this temperature, but by how much?

Since the faulty thermometer consistently reads 10 degrees Celsius higher than the actual temperature, we can subtract 10 from the true temperature to find the reading on the faulty thermometer at the ice point.

So, the reading on the faulty thermometer at the ice point would be:
Ice point reading = True temperature - Calibration offset
Ice point reading = 40 degrees Celsius - 10 degrees Celsius
Ice point reading = 30 degrees Celsius

Therefore, the value of X, representing the ice point of the faulty thermometer, is 30 degrees Celsius.

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