The ice and steam points on a thermometer correspond to X and 50mm respectively. A temperature of 60 °C corresponds to 52 mm on the thermometer. Calculate the value of X
really? 60° reads higher than 100° ?
To calculate the value of X, we need to determine the temperature at the ice point and the corresponding reading on the thermometer.
Given:
- The ice point reading is X mm.
- The steam point reading is 50 mm.
- The temperature reading of 60 °C corresponds to 52 mm on the thermometer.
First, we need to find the temperature range covered by the thermometer. This can be done by subtracting the ice point reading from the steam point reading:
Temperature Range = 52 mm - X mm
We can then calculate the temperature range covered in °C by setting up a proportion:
Temperature Range in mm / Temperature Range in °C = Total Thermometer Range / Total Temperature Range
Since the temperature range on the thermometer corresponds to 60 °C - X °C, we can write the proportion as:
(52 mm - X mm) / (60 °C - X °C) = (50 mm - X mm) / (T - X)
Simplifying, we get:
(52 - X) / (60 - X) = (50 - X) / (T - X)
Cross-multiplying, we get:
(52 - X)(T - X) = (50 - X)(60 - X)
Expanding both sides of the equation, we have:
52T - 52X - XT + X^2 = 50T - 50X - 60X + X^2
Collecting like terms, we get:
52T - XT - 52X + 52X + 50X - 60X = 50T - 60X + X^2 - X^2
Simplifying further, we have:
52T - XT + 50X - 60X + 60X = 50T
Rearranging the equation, we get:
52T - XT = 50T
Subtracting 50T from both sides, we get:
2T - XT = 0
Factoring out T, we have:
T(2 - X) = 0
Since T cannot be zero (as it represents a temperature), we have:
2 - X = 0
Simplifying, we get:
2 = X
Therefore, the value of X is 2.
To calculate the value of X, we need to find the temperature reading on the thermometer when it corresponds to the ice point.
Given that the ice and steam points correspond to X and 50mm respectively, and a temperature of 60 °C corresponds to 52mm on the thermometer, we can set up a proportion:
(X - 0) / (50 - 0) = (60 - 0) / (52 - 0)
Simplifying the equation gives:
X / 50 = 60 / 52
To solve for X, we can cross-multiply:
52X = 60 * 50
Dividing both sides by 52 gives:
X = (60 * 50) / 52
Simplifying further gives:
X = 289.23
Therefore, the value of X is approximately 289.23.