A faulty Celsius thermometer reads 0.7 at the melting point of pure ice and 99.5 degree Celsius at the boiling point of water at normal pressure. (a) what is the correct temperature when it read 60 degree Celsius. (b) at what temperature will it's temperature will be exactly be correct.

a. 0.995T = 60.

T =

100

To solve this problem, we need to find the correction factor for the faulty thermometer that will adjust the readings to the correct temperatures.

(a) To find the correct temperature when the thermometer reads 60 degrees Celsius, we need to determine the correction factor.

First, we calculate the difference between the actual boiling point of water (100 degrees Celsius) and the reading on the faulty thermometer (99.5 degrees Celsius):
100 - 99.5 = 0.5 degrees Celsius

Next, we calculate the difference between the actual freezing point of pure ice (0 degrees Celsius) and the reading on the faulty thermometer (0.7 degrees Celsius):
0.7 - 0 = 0.7 degrees Celsius

Since the boiling point error and the freezing point error have the same magnitude but opposite signs, we can assume a linear relationship between the temperature and the correction factor.

Using this assumption, we can calculate the correction factor for a reading of 60 degrees Celsius:
Correction factor = (60 - 0.7) / (99.5 - 0.7) * (100 - 0.5)
= 59.3 / 98.8 * 99.5
≈ 59.77

The correct temperature, when the faulty thermometer reads 60 degrees Celsius, would be approximately 60 + 59.77 = 119.77 degrees Celsius.

(b) To find the temperature at which the faulty thermometer would display the correct reading, we need to find the point at which the correction factor is 1.

Let's assume the correct temperature is T. Applying the correction factor equation:

Correction factor = (T - 0.7) / (99.5 - 0.7) * (100 - 0.5) = 1

We can simplify this equation to solve for T:

(T - 0.7) / (99.5 - 0.7) * (100 - 0.5) = 1

Now we can solve for T:

(T - 0.7) / 98.8 * 99.5 = 1

(T - 0.7) = 98.8 / 99.5

T = 0.7 + 98.8 / 99.5

By calculating this expression, we find that at a temperature of T ≈ 99.4 degrees Celsius, the faulty thermometer will display the correct reading.

Cright = m Cwrong + b

100 = 99.5 m + b
0 = .7 m + b
----------------------- subtract
100 = 98.8 m
m = 1.01215
0 = .7 (1.01215) +b
b = -0.7085
so
Cright = 1.01215 Cwrong - 0.7085

b. T = 0.995 * 60 =

A sinusoidal a.c.current has a peak value of 5A find: current at an instant when wt=60°and 150°