Question

A faulty thermometer reads $5^{\circ} C$ in melting ice and $95^{\circ} C$ in stream.The correct temperature on absolute scale will be_______ $K$ (when the faulty thermometer reads $41^{\circ} C$).

Answer 1

Correct Answer: 313

To determine the correct temperature on the absolute scale (Kelvin) when a faulty thermometer reads 41°C, we first need to establish the relationship between the faulty thermometer's readings and the actual temperature measurements. The faulty thermometer gives: 

• 5°C for 0°C (melting ice)
• 95°C for 100°C (steam)

We can express this linear relationship by considering the form: \( T_{\text{actual}} = m \cdot T_{\text{faulty}} + c \).

We have two data points to find \( m \) and \( c \):

Faulty (°C)	Actual (°C)
5	0
95	100

Using these points, set up the equations:

• For 5°C: \( 0 = m \cdot 5 + c \)
• For 95°C: \( 100 = m \cdot 95 + c \)

Solving these, subtract the first from the second:

\( 100 = m \cdot 95 + c \)

\( 0 = m \cdot 5 + c \)

Subtract: \( 100 = 90m \)

\( m = \frac{100}{90} = \frac{10}{9} \)

Substitute \( m \) in \( c = 0 - 5m \):

\( c = -5 \times \frac{10}{9} = -\frac{50}{9} \)

Now use the relationship:

\( T_{\text{actual}} = \frac{10}{9} \cdot T_{\text{faulty}} - \frac{50}{9} \)

Set \( T_{\text{faulty}} = 41 \) for conversion:

\( T_{\text{actual}} = \frac{10}{9} \times 41 - \frac{50}{9} \)

\( = \frac{410}{9} - \frac{50}{9} = \frac{360}{9} = 40 \)°C

Convert 40°C to Kelvin:

\( 40 + 273.15 = 313.15 \) K

Rounded to the nearest integer, the actual temperature is 313 K, which falls within the given range [313, 313].