Question

Pressure remaining constant, the density of a gas ______on increasing the temperature.

Answer 1

• According to Charles's law,
• The volume occupied by a fixed amount of gas is directly proportional to its absolute temperature if the pressure remains constant.
• $$\begin{gathered} \mathrm{If} \\ \mathrm{P}=\mathrm{constant} \\ \mathrm{V}\mathrm{is}\mathrm{directly}\mathrm{propotional}\mathrm{to}\mathrm{the}\mathrm{T} \\ \mathrm{that}\mathrm{means} \\ \frac{\mathrm{V}}{\mathrm{T}}=\mathrm{constant} \end{gathered}$$
• If V is replaced by the density term then the equation will be-
• $$\begin{gathered} \mathrm{d}=\frac{\mathrm{m}}{\mathrm{V}} \\ \mathrm{so}, \\ \mathrm{V}=\frac{\mathrm{m}}{\mathrm{d}} \\ \mathrm{putting}\mathrm{the}\mathrm{value}\mathrm{of}\mathrm{density}\mathrm{in}\mathrm{charles}\mathrm{law}\mathrm{we}\mathrm{get} \\ \frac{\mathrm{m}}{\mathrm{d}\times \mathrm{T}}=\mathrm{constnat} \end{gathered}$$
• Here we can see that the density of a given gas at constant pressure is inversely proportional to its temperature.
• $\frac{\mathrm{m}}{\mathrm{d}}=T$
• So, if at the constant pressure-temperature rises then the density will decrease.