Question

The macroscopic properties of gases include its pressure (P), volume (V), its temperature (T), the quantity of the gas, which can be measured by its mass (M), or the number of gas particles (atoms/molecules; N). One of the earliest investigations on a relationship between these properties was conducted by Robert Boyle, chiefly motivated by a hunch against one of his contemporary, Toricelli's claim on how a barometer works. Boyle's set-up was as shown.

He attached a small U-tube at the end of a Toricellian tube and powered in mercury from the open end (T); as mercury rose in the closed, shorter column, the trapped air would get more and move compressed - which could only mean, that the pressure increased, and the volume decreased (these were respectively measured by the height of the mercury column, h, and a scale on the shorter column, V, for volume of the trapped air).

Which of these statements is/are correct in regard to Boyle's conclusion from the data?

• A. The height difference of the two levels is directly proportional to the pressure of the trapped air
• B. As the value of h increased, V monotonically decreased
• C. If we blow air through the open end of T, then h would be a bad measure for the pressure of the trapped air
• D. The graph of h versus the reciprocal of V is a straight line

Answer 1

Answer: (A), (B), (C), (D)

The graph of h versus the reciprocal of V is a straight line

Boyle concluded his experiment with the following results -

(i) The pressure of the trapped gas will be the pressure on the mercury in the shorter column, P, given by $P=P_0+\rho gh$, where $P_0$ is1 atm and $\rho$, the density of mercury. Thus, P is directly proportional to h, but with a P-intercept of $P_0$. (ii) As more mercury was added, P increased (with $\rho gh$); at the same time, the level in the shorter column went up, thus decreasing the volume of trapped air, V. (iii) He plotted the varying, pressure P against V, and $\left(\frac{1}{V}\right)$, and obtained the following trends

(iv) Astonishingly, the graph of P versus $\left(\frac{1}{V}\right)$ was, more or less, a straight line for a fixed temperature.

This result, which later got identified as Boyle's law, is stated as -

$p\propto \left(\frac{1}{V}\right)$

PV= constant (at a certain temperature)>

He published this major result in 1660, along with details of his experiments, in one of his first books "New Experiments, Physico Mechanical”.