Question

At constant temperature, in a given mass of an ideal gas
A) The ratio of pressure and volume always remains constant
B) The volume remains constant
C) Pressure always remains constant
D) Product of pressure and volume remains constant

Answer 1

Boyle’s law; at constant temperature, the pressure of a given mass of gas is inversely proportional to its volume.
$P \propto (1/V)$
$\Rightarrow P = \dfrac{k}{V}$

Complete step by step solution:
From the given equation of Boyle’s law, it states that
$PV = K$
It means that the product of pressure and volume remains constant. The law can be derived from the kinetic theory of gases assuming a perfect (ideal) gas.
Real gases obey Boyle’s law at sufficiently low pressures, although the product pv generally decreases slightly at higher pressures, where the gas begins to depart from ideal behaviour.

**Hence, option “D” is correct

Note: **
Formulated in 1662, Boyle’s Law states that the pressure (p) of a given quantity of gas varies inversely with its volume (v) at constant temperature; i.e., in equation form, $PV = K$ , a constant.
The product of pressure and volume is exactly a constant for an ideal gas.
${P_1}{V_1} = {P_2}{V_2}$
This equation can be used to predict the increase in the pressure exerted by a gas on the walls of its container when the volume of its container is decreased.