Answer:
At [tex]\displaystyle\bf58\frac{1}{3}^o[/tex], the faulty Celsius thermometer will have the correct reading. (which means the standard Celsius thermometer also have the same reading)
Explanation:
We can find the temperature which both the faulty and standard Celsius thermometers have the same reading by matching their:
- melting points
- boiling points
- scale
Let the faulty Celsius thermometer's readings in °X, whereas the standard Celsius thermometer's readings in °C
Given:
- melting points: 0°C = 0.7°X
- boiling points: 100°C = 99.5°X
- scale: (100 - 0)°C = (99.5 - 0.7)°X
100°C = 98.8°X
1°C = 0.988°X
Let the same reading is n°C. Then, the reading at the faulty thermometer is also n°X
To convert n°C into °X:
[tex]\boxed{n^oC = (0.988n + 0.7)^oX}[/tex]
[tex]n^oC=n^oX[/tex]
[tex](0.988n + 0.7)^oX=n^oX[/tex]
[tex]n-0.988n=0.7[/tex]
[tex]n=0.7\div0.012[/tex]
[tex]\displaystyle=58\frac{1}{3}[/tex]
