a thermometer records 680 mmHg at steam point and 440 mmHg at ice point. The temperature it records at 380 mmHg is

Analyze the question

This is a thermometer that uses a physical property (here, pressure in mmHg) to measure temperature. The fixed points are:

• Steam point (100°C): 680 mmHg
• Ice point (0°C): 440 mmHg

We need the temperature when the reading is 380 mmHg.

Concept

For a linear thermometric property, the temperature is:

θ = [(X_θ − X_ice) / (X_steam − X_ice)] × 100°C

Solution

• X_θ − X_ice = 380 − 440 = −60
• X_steam − X_ice = 680 − 440 = 240

θ = (−60 / 240) × 100 θ = −0.25 × 100 θ = −25°C

The reading of 380 mmHg is below the ice-point reading of 440 mmHg, so the temperature must be below 0°C. That means the answer has to be negative, which rules out C and D straight away.

Tip

Always use the formula (reading − lower fixed point) ÷ (upper fixed point − lower fixed point) × 100. Then check the sign: if the reading is below the ice-point value, the temperature is negative.