Multiple choice general knowledge science & technology

The lengths of mercury thread in the stem of a mercury thermometer are given in three situations. length in melting ice = 20 mm length in steam above boiling water = 170 mm length in liquid X = 50 mm What is the temperature of liquid X in degrees centigrade?

  1. 40 degree C

  2. 30 degree C

  3. 20 degree C

  4. 10 degree C
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Using the linear scale formula: $T = \frac{L_x - L_{ice}}{L_{steam} - L_{ice}} \times 100$. Here, $\frac{50 - 20}{170 - 20} \times 100 = \frac{30}{150} \times 100 = 0.2 \times 100 = 20$. Thus, the temperature is 20 degrees Celsius.

AI explanation

To determine the temperature of liquid X, we need to use the principle of the mercury thermometer.

The principle states that the length of the mercury thread in the stem of a mercury thermometer is directly proportional to the temperature of the substance being measured.

Let's assign variables to the lengths of the mercury thread in each situation:

  • Length in melting ice: $L_1 = 20 \, \text{mm}$
  • Length in steam above boiling water: $L_2 = 170 \, \text{mm}$
  • Length in liquid X: $L_3 = 50 \, \text{mm}$

Now, we can set up a proportion to find the temperature of liquid X. The proportion is as follows:

$$\frac{L_3 - L_1}{L_2 - L_1} = \frac{T_3 - T_1}{T_2 - T_1}$$

Where:

  • $T_1$ is the temperature in melting ice
  • $T_2$ is the temperature in steam above boiling water
  • $T_3$ is the temperature of liquid X

Substituting the given values: $$\frac{50 - 20}{170 - 20} = \frac{T_3 - 0}{100 - 0}$$

Simplifying the equation: $$\frac{30}{150} = \frac{T_3}{100}$$

Cross multiplying: $$30 \times 100 = 150T_3$$

Solving for $T_3$: $$T_3 = \frac{30 \times 100}{150}$$

Simplifying the expression: $$T_3 = 20 \, \text{degrees C}$$

Therefore, the temperature of liquid X is 20 degrees Celsius.

The correct answer is option C) 20 degrees C.

Keep practicing — related questions