The ice point of an ungraduated mercury in glass thermometer is x Y is steam point is 90° this thermometer reads 60° when the true temperature is 40° C calculate the value of x
To calculate the value of x, we need to determine the difference between the ice point and the steam point on the thermometer.
Given that the ice point is x and the steam point is 90°, the difference would be 90° - x.
Since the thermometer reads 60° when the true temperature is 40°C, the difference between the reading and the true temperature is 60° - 40°C = 20°C.
We can set up the following equation:
[true temperature (40°C) - ice point (x)] / [steam point (90°) - ice point (x)] = difference (20°C) / difference on the thermometer (90° - x)
Using the equation above, we can solve for x:
(40°C - x) / (90° - x) = 20°C / (90° - x)
Cross-multiplying:
20°C (90° - x) = (40°C - x) (90° - x)
1800°C - 20x°C = 3600°C - 40x°C + x²
Rearranging the equation and moving all terms to one side:
x² - 20x°C - 1800°C + 3600°C - 1800°C = 0
x² - 20x°C + 1800°C = 0
Applying the quadratic formula:
x = [-(-20) ± √((-20)² - 4(1)(1800))] / (2 * 1)
x = [20 ± √(400 - 7200)] / 2
x = [20 ± √(-6800)] / 2
Since we cannot take the square root of a negative number, there are no real solutions for x in this case.