Question

The length of mercury thread in a thermometer at 100° C and 50°C is 10 cm and 4 cm, respectively. What is the length of the mercury thread when it is kept in contact with melting ice?

• A. 0
• B. 2 cm
• C. 1 cm
• D. 3 cm

Answer 1

The correct option is B

2 cm

Step 1: Given Data

Length of mercury thread at ${100}^{0}C=10cm$

Length of mercury thread at ${50}^{0}C=4cm$

The temperature of melting ice $=0^{0}C$

Let the length of the mercury thread when it is kept in contact with melting ice be $x$

Step 2 : Calculation:

The ratio of mercury column lengths to the temperatures is given by

$\frac{T_{100}-T_0}{T_{\theta }-T_0}=\frac{l_{100}-l_0}{l_{\theta }-l_0}$ where $T_{100}{T}_0$represents the boiling and freezing point of water respectively and $l_{100}{l}_0$represents the length of the mercury in

the thermometer at these two temperatures. Here $\theta ={50}^{0}C$ at which respective length of the mercury column is given.

On substituting values we get,

$\begin{array}{l}\Rightarrow \frac{100-0}{50-0}=\frac{10-x}{4-x}\\ \Rightarrow 2=\frac{10-x}{4-x}\end{array}$

$\begin{array}{l}\Rightarrow 2\left(4-x\right)=10-x\\ \Rightarrow 8-2x=10-x\\ \Rightarrow x=-2\end{array}$

So, the length of the mercury thread when kept in melting ice is $2cm$

Thus, the correct option is (b).