Name: Specific Heat Capacity of Water
Uploaded: 2019-07-19
Duration: 6 min 44 s
Description: Due to a lack of electricity, sometimes, we keep our cold drinks in water to maintain their coldness. Why? Because it takes time to draw heat out of water. W...

Question

Draw the approximate plots of isochoric, isobaric, isothermal and adiabatic processes, for the case of an ideal gas, using the following variables,

(a) P, T (b) V, T

Accepted Answer

$(a) P, T (b) V, T$ Ideal gas law is given by, $P V = n R T$ .

$P = (\frac{n R}{V}) T = k T$ (where, $k = \frac{n R}{V}$ )

For isochoric process, $V =$ constant, so $k = \frac{n R}{V} =$ constant. Thus, $P = k T$ represents a straight line passing through the origin and its slope is $k$ .

For isobaric process, $P =$ constant. Thus, on $P - T$ curve, it is a horizontal straight line parallel to $T$ -axis, if $T$ is taken along the horizontal (or $x$ -axis).

For isothermal process, $T =$ constant. Thus, on $P - T$ curve, it represents a vertical straight line, if $T$ is taken along the horizontal (or $x$ -axis).

For adiabatic process, $T^{γ} P^{1 - γ} =$ constant,
or, $T^{\frac{γ}{1 - γ}} P = constant$ $\dots (1)$
Because $γ > 1$ , so $1 - γ < 0$ and $\frac{1 - γ}{γ} < 0$
Suppose $\frac{1 - γ}{γ} = - B$

From equation (1),
$T^{- B} P =$ Constant $= C$ (say)
$\frac{P}{T^{B}} = C P = C T^{B}$
Because $0 < B < 1$ , so the graph is

$(b)$ As $P$ is not considered as a variable, we have, from the ideal gas law,

$P V = n R T$

$V = \frac{n R}{P} T = k' T$ (where, $k' = \frac{n R}{P}$ )

On $V - T$ coordinate system, let us take $T$ along $x$ -axis.

For isobaric process, $P =$ constant. In $V = k' T$ , $k'$ will be constant. The graph will be,

For isochoric process, $V =$ constant. $V = k^{'} T$ obviously represents a straight line parallel to $T$ -axis.

For isothermal process, $T =$ constant. Thus, on the stated coordinate system it represents a straight line, parallel to the $V$ -axis.

For adiabatic process, $T V^{γ - 1} =$ constant
$0 < γ - 1 < 1$

Draw the approximate plots of isochoric, isobaric, isothermal and adiabatic processes, for the case of an ideal gas, using the following variables,
$(a) P, T (b) V, T$

Important Questions on THERMODYNAMICS AND MOLECULAR PHYSICS

Learn and Prepare for any exam you want !

Draw the approximate plots of isochoric, isobaric, isothermal and adiabatic processes, for the case of an ideal gas, using the following variables, (a) P, T(b) V, T

Important Questions on THERMODYNAMICS AND MOLECULAR PHYSICS

Learn and Prepare for any exam you want !

Draw the approximate plots of isochoric, isobaric, isothermal and adiabatic processes, for the case of an ideal gas, using the following variables,
$(a) P, T (b) V, T$