Question

For a given amount of gas showing ideal behaviour, draw labelled graphs of:

(a) The variation of\(P\)with\(V\)

(b) The variation of \(V\)with\(T\)

(c) The variation of \(P\)with\(T\)

(d) The variation of \(\frac{1}{P}\)with\(V\)

Short answer

a.

The labelled graph of variation of \(P\) with \(V\):

b.

The labelled graph of the variation of \(V\)with \(T\):

c.

The labelled graph of the variation of \(P\)with \(T\):

d.

The labelled graph of the variation of \(\frac{1}{P}\)with \(V\):

Step-by-step solution

Definition of graph

A graph is a structure consisting of a collection of elements, some of which are "connected" in some way.

Graph of the variation of \(P\)with\(V\)

a)

Sketch a graph.

Ideal gas equation= \(PV = nRT\)

\(PV = \)Constant at a constant \(T\)and \(n.P\) is inversely proportional \(V\).

\(P\alpha \frac{1}{V}\)

Hence, by considering the given problem and Ideal gas equation graph is drawn.

Graph of the variation of \(V\)with \(T\)

b)

Consider the given problem and solve.

Ideal gas equation= \(PV = nRT\)

\(\frac{V}{T} = \)Constant at constant \(P\) and \(n.V\)is directly proportional to \(T.V\alpha T{\rm{.}}\)

Therefore, by considering the given problem and Ideal gas equation graph is drawn.

Graph of the variation of \(P\)with\(T\)

c)

Let us solve the given problem.

Ideal gas equation= \(PV = nRT\)

\(\frac{P}{T} = \)Constant at constant \(V\)and \(n{\rm{ }}.{\rm{ }}P\;\) is directly proportional to\(T\).

Hence, by considering the given problem and Ideal gas equation graph is drawn.

Graph of the variation of \(\frac{1}{P}\)with \(V\)

d)

Sketch the graph of the given variation.

Ideal gas equation= \(PV = nRT\)

P V= constant at a constant Tand \(n\)\(\frac{1}{P}\)is directly proportional \(V\)\(.\frac{1}{P}\alpha V\).

Therefore, by considering the given problem and Ideal gas equation graph is drawn.