A faulty celcius thermometer read 0.7 degree celcius at the melting point of pure ice and 99.5 at the boiling point of water at normal pressure.
Calculate the correct temperature when it reads 30 degree celcius.
At what temperature will its reading be exactly correct
99.5-.7 = 98.8
so
Reading C = Cr = .7 +(98.8/100) C
if Cr = 30
30 = .7 + .988 C
C = 29.7
if the same
C = .7 + .988 C
.012 C = .7
C = 58.3 degrees C or Cr
physics
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To calculate the correct temperature when the faulty thermometer reads 30 degrees Celsius, we need to find the relationship between the faulty readings and the correct temperatures.
Given:
Faulty reading at the melting point of pure ice: 0.7 degrees Celsius
Faulty reading at the boiling point of water: 99.5 degrees Celsius
To find the correct temperature when the faulty reading is 30 degrees Celsius, we first need to determine the range of the faulty readings.
The range of the faulty readings can be calculated by subtracting the melting point reading from the boiling point reading:
Range = Boiling point reading - Melting point reading
Range = 99.5 - 0.7 = 98.8 degrees Celsius
Next, we need to calculate the faulty reading as a fraction of the total range:
Faulty reading as a fraction = (Faulty reading - Melting point reading) / Range
Faulty reading as a fraction = (30 - 0.7) / 98.8
Now, we can use this fraction to find the correct temperature. Multiply the fraction by the range and add it to the melting point reading:
Correct temperature = (Faulty reading as a fraction * Range) + Melting point reading
Correct temperature = ((30 - 0.7) / 98.8) * 98.8 + 0.7
Simplifying the equation, we get:
Correct temperature = (29.3 / 98.8) * 98.8 + 0.7
Correct temperature = 29.3 + 0.7
Correct temperature = 30 degrees Celsius
Therefore, when the faulty thermometer reads 30 degrees Celsius, the correct temperature is also 30 degrees Celsius.
To determine the temperature at which the thermometer's reading will be exactly correct, we need to find the measurement error at different temperature levels.
From the given information, we know that the thermometer reads 0.7 degrees Celsius lower than the actual temperature at the melting point of pure ice. So, at this point, the thermometer's error is -0.7 degrees Celsius.
To determine the temperature at which the thermometer's reading will be exactly correct, we need to find the point where the error balances out. Since the thermometer reads 0.7 degrees Celsius lower than the actual temperature at the melting point, it will also read 0.7 degrees Celsius higher than the actual temperature at some other point.
To find the exact temperature at which this occurs, we need to solve the equation:
Faulty reading - Correct temperature = 0.7
Using the faulty reading formula:
(Faulty reading - Melting point reading) / Range = 0.7 / Range
Simplifying the equation, we get:
Faulty reading - Melting point reading = 0.7
Faulty reading = 0.7 + Melting point reading
Now, we can substitute the values:
Faulty reading = 0.7 + 0.7 = 1.4 degrees Celsius
This means that, when the faulty thermometer reads 1.4 degrees Celsius, its reading will be exactly correct.
Therefore, the temperature at which the thermometer's reading will be exactly correct is 1.4 degrees Celsius.