Question

A gas thermometer measures the temperature from the variation of pressure of a sample of gas. If the pressure measured at the melting point of lead is 2.20 times the pressure measured at the triple point of water, find the melting point of lead.
A) 600K
B) 420K
C) 790 K
D) 510K

Answer 1

Hint: We can use the given statement to form an equation, this equation can be used for substituting the values in the formula to calculate the melting point. We didn’t substitute the value of pressure at triple point because it was a common quantity in both the equations and thus could easily get cancelled.Thus, we will be able to find the required value.

Formula used:
$M.P = \dfrac{{{P_{MP}}}}{{{P_{TP}}}} \times 273.16K$ where, M.P is melting point, ${P_{MP}}$ is the pressure at melting point, ${P_{TP}}$ is the pressure measured at triple point and K represents the unit Kelvin.

Complete step by step answer:
It is given that the pressure measured at melting point $\left( {{P_{MP}}} \right)$ of lead is 2.20 times the pressure measured at the triple point of water $\left( {{P_{TP}}} \right)$
$ \Rightarrow {P_{MP}} = 2.2 \times {P_{TP}}....(1)$
Melting point (M.P) of lead can be calculated by the division of pressure measured at its melting point by the triple point of water and multiplied by 273.16K.
$ \Rightarrow M.P = \dfrac{{{P_{MP}}}}{{{P_{TP}}}} \times 273.16K$
Substituting the value from (1), we have:
\[
\Rightarrow M.P = \dfrac{{2.2 \times {P_{TP}}}}{{{P_{TP}}}} \times 273.16K \\
\Rightarrow M.P = \left( {2.2 \times 273.16} \right)K \\
\Rightarrow M.P = 600.952K \approx 600K \\
 \]
Therefore, the melting point of lead is approximately 600 K

So, the correct answer is “Option A”.

Note:
The triple point of water mentioned in the question means the pressure at which it is co-existing in all the three states, liquid, solid and gas, for water it is 273.16K in magnitude.
The calculated value of melting point can be rounded off to both 601 K (preferably) and 600K, but we approximated it using the sign $' \approx '$ to 600K so as to match the options given. The formula used here is a known and general formula