JEE Main & Advanced Physics Thermodynamical Processes Isobaric Process

When a thermodynamic system undergoes a physical change in such a way that its pressure remains constant, then the change is known as isobaric process.

(1) Equation of state : In this process V and T changes but P remains constant. Hence Charle?s law is obeyed in this process.

Hence if pressure remains constant  \[V\propto T\Rightarrow \frac{{{V}_{1}}}{{{T}_{1}}}=\frac{{{V}_{2}}}{{{T}_{2}}}\]

(2) Indicator diagram : Graph 1 represent isobaric expansion, graph 2 represent isobaric compression.

Slope =\[\frac{dP}{dV}=0\]            Slope = \[\frac{dP}{dV}=0\]

(i) In isobaric expansion (Heating) 

Temperature \[\xrightarrow{\,\,\,\,}\] increases so \[\Delta U\] is positive

Volume \[\xrightarrow{\,\,\,\,}\] increases so \[\Delta W\] is positive

Heat \[\xrightarrow{\,\,\,\,}\] flows into the system so \[\Delta Q\] is positive

(ii) In isobaric compression (Cooling)

Temperature \[\xrightarrow{\,\,\,\,}\] decreases so \[\Delta U\] is negative

Volume \[\xrightarrow{\,\,\,\,}\] decreases so \[\Delta W\] is negative

Heat \[\xrightarrow{\,\,\,\,}\] flows out from the system so \[\Delta Q\] is negative

(3) Specific heat : Specific heat of gas during isobaric process \[{{C}_{P}}=\left( \frac{f}{2}+1 \right)R\]

(4) Bulk modulus of elasticity : \[K=\frac{\Delta P}{\frac{-\Delta V}{V}}=0\] [As \[\Delta P=0\]]

(5) Work done in isobaric process

\[\Delta W=\int_{{{V}_{i}}}^{{{V}_{f}}}{P\,dV}=P\int_{{{V}_{i}}}^{{{V}_{f}}}{dV}=P[{{V}_{f}}-{{V}_{i}}]\]                [As P = constant]

\[\Rightarrow \] \[\Delta W=P({{V}_{f}}-{{V}_{i}})=\mu R[{{T}_{f}}-{{T}_{i}}]=\mu R\,\Delta T\]

(6) FLOT in isobaric process : From  \[\Delta Q=\Delta U+\Delta W\]

\[\because \] \[\Delta U=\mu \,{{C}_{V}}\,\Delta T\]\[=\mu \frac{R}{(\gamma -1)}\Delta T\] and  \[\Delta W=\mu R\,\Delta T\]

\[\Rightarrow \] \[{{(\Delta Q)}_{P}}=\mu \frac{R}{(\gamma -1)}\Delta T+\mu R\,\Delta T\]\[=\mu \left( \frac{\gamma }{\gamma -1} \right)R\,\Delta T\]\[=\mu \,{{C}_{P}}\,\Delta T\]

(7) Examples of isobaric process : All state changes occurs at constant temperature and pressure.

Boiling of water

(i) Water \[\xrightarrow{\,}\] vapours

(ii) Temperature \[\xrightarrow{{}}\] constant

(iii) Volume \[\xrightarrow{\,}\]increases

(iv) A part of heat supplied is used to change volume (expansion) against external pressure and remaining part is used to increase it's potential energy (kinetic energy remains constant)

(v) From FLOT \[\Delta Q=\Delta U+\Delta W\Rightarrow mL=\Delta U+P({{V}_{f}}-{{V}_{i}})\]

Freezing of water

(i) Water \[\xrightarrow{\,}\] ice

(ii) Temperature \[\xrightarrow{\,}\] constant

(iii) Volume \[\xrightarrow{\,}\]increases

(iv) Heat is given by water it self. It is used to do work against external atmospheric pressure and to decreases the internal potential energy.

(v) From FLOT \[\Delta Q=\Delta U+\Delta W\Rightarrow -mL=\Delta U+P({{V}_{f}}{{V}_{i}})\]