Thermodynamics Concept Page - 9

Definition

Isochoric process

An isochoric process is a thermodynamic process during which the volume of the closed system undergoing such a process remains constant. An isochoric process is exemplified by the heating or the cooling of the contents of a sealed, inelastic container

Definition

Work done in an isochoric process

W=∫PdV$W=\int PdV$
Here dV=0$dV=0$. ∴W=0$\therefore W=0$

Diagram

PV,TV,PT diagrams for an isochoric process

Definition

Reversible process

A thermodynamic process is reversible if the process can be turned back such that both the system and the surroundings return to their original states, with no other change anywhere else in the universe.
Example: two metal jars A and B are at a thermal equilibrium and are in contact with each other. Now when we heat jar A slightly, heat starts to flow from Jar A to Jar B. This is the direction of this process. Now this process can be reversed just by cooling Jar A slightly. When Jar A is cooled, heat flows from Jar B to Jar A till thermal equilibrium is reached.

Definition

Irreversible process

A process is said to be irreversible if it cannot return the system and the surroundings to their initial states when the process is reversed. The irreversible process is not at equilibrium throughout the process.For example, free expansion of a fluid

Definition

Isothermal process

An isothermal process is one in which the temperature is constant.

Diagram

PV diagram of an isothermal process

Formula

Work done in an isothermal process

W=PVln(V2/V1)=nRTln(V2/V1)=nRTln(P1/P2)$W=PVln(V_2/V_1)=nRTln(V_2/V_1)=nRTln(P_1/P_2)$

Definition

Adiabatic process

In an adiabatic process, the system is insulated from the surroundings and heat absorbed or released is zero. For an adiabatic process of an ideal gas,
PVγ=constant$P{V}^{\gamma }=constant$
where γ$\gamma$ is the ratio of specific heats (ordinary or molar) at constant pressure and at constant volume.
γ=CpCv$\gamma ={\displaystyle \frac{C_p}{C_v}}$

Example

P-V relation for an adiabatic process

For an adiabatic process, δQ=0⇒−δW=δU$\delta Q=0\Rightarrow -\delta W=\delta U$
⇒−PδV=fnRδT=f(PδV+VδP)$\Rightarrow -P\delta V=fnR\delta T=f(P\delta V+V\delta P)$ 
On simplification and putting γ=f+1f$\gamma ={\displaystyle \frac{f+1}{f}}$ we get PVγ=constant$P{V}^{\gamma }=constant$
Example :
A polyatomic gas (γ=43)$(\gamma ={\displaystyle \frac{4}{3}})$ is compressed to 18${\displaystyle \frac{1}{8}}$ of its volume adiabatically. If its initial pressure is P, the new pressure will be:In an adiabatic process we have P×Vγ$P\times V^{\gamma }$ constant .
or
Pf=P(V1V2)43$P_f=P({\displaystyle {\displaystyle \frac{V_1}{V_2}}{)}^{{\displaystyle \frac{4}{3}}}}$
Therefore if V$V$ become 18${\displaystyle \frac{1}{8}}$ . Substituting values in the equation will give final P to be 16P$16P$.

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