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Adiabatic process is considered one the most difficult concept.
68 Questions around this concept.
When a gas expands adiabatically
A given system undergoes a change in which the work done by the system equals the decrease in its internal energy. The system must have undergone an
During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio for the gas is
NEET 2025: Syllabus | Most Scoring concepts | NEET PYQ's (2015-24)
A P-V diagram for an ideal gas for the different processes is shown. In graph curve OR represents:
For an adiabatic process which of the following statement is not true
For a thermodynamic process, specific heat of gas is zero. The process is
If and
represent the increase in internal energy and work done by the system respectively in a thermodynamical process, which of the following is true?
Trusted by 3,500+ universities and colleges globally | Accepted for migration visa applications to AUS, CAN, New Zealand , and the UK
In thermodynamic processes, which of the following statements is not true?
The internal energy change in a system that has absorbed 2 kcals of heat and done 500 J of work is;
A monoatomic gas at a pressure P, having a volume V expands isothermally to a volume 2 V, and then adiabatically to a volume 16 V. The final pressure of the gas is:
Adiabatic process -
When a thermodynamic system undergoes a process, such that there is no exchange of heat takes place between the system and surroundings, this process is known as the adiabatic process.
In this process $\mathrm{P}, \mathrm{V}$, and T change but $\Delta Q=0$.
From the first law of thermodynamics -
$$
\Delta Q=\Delta U+\Delta W
$$
Now in adiabatic -
$$
0=\Delta U+\Delta W
$$
So, $\Delta U=-\Delta W$ for the adiabatic process
Now, let us take two cases, the first is for expansion in which the work done is positive and the second one is compression in which the work done is negative -
If $\Delta W=$ positive then $\Delta U$ becomes negative so temperature decreases ie., adiabatic expansion produces cooling.
If $\Delta W=$ negative then $\Delta U$ becomes positive so temperature increases ie., adiabatic compression produces heating.
Equations of Adiabatic process -
1. $P V^\gamma=$ constant; where $\gamma=\frac{C_P}{C_V}$ -- -- Relating Pressure and volume
2. $T V^{\gamma-1}=$ constant $\Rightarrow T_1 V_1^{\gamma-1}=T_2 V_2^{\gamma-1}$ or $T \propto V^{1-\gamma}---$ - -Relating Temperature and volume
3. $\frac{T^\gamma}{P^{\gamma-1}}=$ const. $\Rightarrow T_1^\gamma P_1^{1-\gamma}=T_2^\gamma P_2^{1-\gamma}$ or $T \propto P^{\frac{\gamma-1}{\gamma}}$ or $P \propto T^{\frac{\gamma}{\gamma-1}}$
For the slope of the adiabatic curve on the PV curve, we have to differentiate the adiabatic relation -
As, $P V^\gamma=$ constant
So,
$$
\begin{aligned}
& d P V^\gamma+P \gamma V^{\gamma-1} d V=0 \\
& \frac{d P}{d V}=-\gamma \frac{P V^{\gamma-1}}{V^\gamma}=-\gamma\left(\frac{P}{V}\right)
\end{aligned}
$$
So we can say that in the given graph, the slope $=$
$$
\tan \phi=-\gamma\left(\frac{P}{V}\right)
$$
Also, we have studied that the slope of the isothermal curve on the PV diagram is = So, we can say that the - $\quad$ (Slope $)_{\text {adiabatic }}=\gamma \times(\text { Slope })_{\text {isother mal }}$, or $\frac{(\text { Slope })_{\text {adiabatic }}}{(\text { Slope })_{\text {isother mal }}}>1$
With the help of the graph we can see that the adiabatic curve is steeper than the isothermal curve-
or,
Specific heat in adiabatic process - The specific heat of a gas during adiabatic change is zero. Mathematically -
$$
C=\frac{Q}{m \Delta T}=\frac{0}{m \Delta T}=0 \quad[\text { As } Q=0]
$$
Note Even though heat is not supplied or taken out during the process but still, the temperature change is taking place. So we can say that the Specific heat for an adiabatic process is zero.
Work done in adiabatic process -
$$
W=\int_{V_i}^{V_f} P d V=\int_{V_i}^{V_f} \frac{K}{V^\gamma} d V \Rightarrow W=\frac{\left[P_i V_i-P_f V_f\right]}{(\gamma-1)}=\frac{\mu R\left(T_i-T_f\right)}{(\gamma-1)}
$$
$\mathrm{Sa}_1$ if $\gamma$ is increasing then work done will be decreasing. As we know that -
$$
\because \gamma_{\text {mono }}>\gamma_{\text {diatomic }}>\gamma_{\text {triatomic }} \Rightarrow W_{\text {mono }}<W_{\text {diatomic }}<W_{\text {triatomic }}
$$
Elasticity in adiabatic process - As, $P V^\gamma=$ constant
Differentiating both sides of the above equation, we get - $d P V^\gamma+P \gamma V^{\gamma-1} d V=0$
$$
\gamma P=\frac{d P}{-d V / V}=\frac{\text { Stress }}{\text { Strain }}=E_\phi \Rightarrow E_\phi=\gamma P
$$
i.e. adiabatic elasticity is $\gamma$ times that of pressure
$$
E_\theta=P \Rightarrow \frac{E_\phi}{E_\theta}=\gamma=\frac{C_p}{C_V}
$$
i.e. the ratio of two elasticity of gases is equal to the ratio of two specific heats.
Where,
$$
\begin{aligned}
& \quad E_\phi=\text { Elasticity in adiabatic process } \\
& \text { and } \\
& E_\theta=\text { Elasticity in isothermal process }
\end{aligned}
$$
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