Question

The higher and the lower fixed points on the thermometer are separated by 160mm. when the length of mercury thread above the lower temperature is 40mm ,the temperature reading would be

Answer 1

Answer :

Difference b/w UFP and LFP = 160mm

We have to find temperature reading (in °C) when the length of mercury thread above the lower temperature is 40mm$.$

★ For any temperature measuring scale,

$\dag\:\boxed{\bf{\dfrac{R-LFP}{UFP-LFP}=constant}}$

• R denotes reading of temperature
• UFP denotes upper fixed point
• LFP denotes lower fixed point

★ For celsius scale,

• UFP = 100
• LFP = 0
• UFP - LFP = 100

Now coming to the question,

For a new temperature measuring scale

• UFP - LFP = 160
• LFP = 0

★ Calculation :

$\implies\sf\:\dfrac{R_{mm}-LFP}{UFP-LFP}=\dfrac{R_{(^{\circ} C)}-LFP}{UFP-LFP}$

$\implies\sf\:\dfrac{40-0}{160}=\dfrac{R_{(^{\circ} C)}-0}{100}$

$\implies\sf\:\dfrac{40\times 100}{160}=R_{(^{\circ} C)}$

$\implies\sf\:R_{(^{\circ} C)}=\dfrac{100}{4}$

$\implies\bf\:R_{(^{\circ} C)}=25^{\circ}C$

Answer 2

Given :-

• Higher fixed point (HFP) = 160 mm

• Lower fixed point (LFP) = 0 mm

That's why there is difference in separation i.e. 160 mm

• New fixed point (NFP) = 40 mm

As per the formula,

(NFP - LFP)/(UFP - LFP) = C/100

Here, C is the temperature in celcius.

(40 - 0)/(160 - 0) = C/100

40/160 × 100 = C

C = 100/4

C = 25°C

Hence,

The temperature reading = C = 25°C