Name: First Law of Thermodynamics
Uploaded: 2019-07-19
Duration: 6 min 30 s
Description: The first law of thermodynamics is explained with an example. The video defines the thermodynamic system and surrounding and identifies the work done by the...

Question

The pressure versus temperature $(p - T)$ graph of $n moles$ of an ideal gas is shown in the figure. Plot the corresponding,
$(a)$ density versus volume $(ρ - V)$ graph
$(b)$ pressure versus volume $(p - V)$ graph and
$(c)$ density versus pressure $(ρ - p)$ graph.

Accepted Answer

From the given $P - T$ diagram,

$n moles$ and $C \to D$ is an isothermal process and

$(ρ - V)$ and $D \to A$ is an isochoric process.

Ideal gas equation, $P V = n R T$ .

In an isothermal process, $(c)$ and $(ρ - p)$ ,

Temperature, $T$ is constant, thus, $P V = constant$

that is, $P \propto \frac{1}{V} . . . (1)$ .

So, $P - V$ diagram will be a rectangular hyperbola.

Since, the mass of a gas remains constant in a process.

$V ρ = constant$

$ρ \propto \frac{1}{V} . . . (2)$ .

So, $ρ - V$ diagram will also be a rectangular hyperbola.

From equations $(1)$ and $(2)$ , we can write,

$ρ \propto P$ .

So, the $ρ - P$ diagram will be a straight line with a non-zero slope.

In an isochoric process, $B \to C$ and $D \to A$ ,

Volume, $V \to constant$ .

So, $P - V$ diagram is a straight line parallel to the axis of volume.

Since, mass, $m = V ρ$ and as both $m$ and $V$ are constants.

$ρ \to constant$ .

So, $ρ - V$ diagram will lie in the same state at $B$ and $C$ and at $D$ and $A$ .

Since density $ρ \propto \frac{1}{V}$ and volume $V$ is constant in the process $B \to C$ and $D \to A$ .

$ρ$ is also constant and thus, $ρ - P$ diagram is a straight line parallel to the axis of the density.

With the information obtained above,

$(a)$ The density versus volume $(ρ - V)$ graph is,

$(b)$ The pressure versus volume $(P - V)$ graph is,

$(c)$ The density versus pressure $(ρ - P)$ graph is,

The pressure versus temperature $(p - T)$ graph of $n moles$ of an ideal gas is shown in the figure. Plot the corresponding,
$(a)$ density versus volume $(ρ - V)$ graph
$(b)$ pressure versus volume $(p - V)$ graph and
$(c)$ density versus pressure $(ρ - p)$ graph.

Important Questions on Laws of Thermodynamics

Learn and Prepare for any exam you want !

The pressure versus temperature (p-T) graph of n moles of an ideal gas is shown in the figure. Plot the corresponding, (a) density versus volume (ρ-V) graph (b) pressure versus volume (p-V) graph and (c) density versus pressure (ρ-p) graph.

Important Questions on Laws of Thermodynamics

Learn and Prepare for any exam you want !

The pressure versus temperature $(p - T)$ graph of $n moles$ of an ideal gas is shown in the figure. Plot the corresponding,
$(a)$ density versus volume $(ρ - V)$ graph
$(b)$ pressure versus volume $(p - V)$ graph and
$(c)$ density versus pressure $(ρ - p)$ graph.