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21 Questions around this concept.
In the given diagram graph 1 represents the adiabatic process and 2 represents the isothermal process. Which of the following comparisons is not true for graphs 1 and 2
The Thermodynamic process, in which the internal energy of the system remains constant is
For the P-V diagram given for an ideal gas,
out of the following which one correctly represents the T-P diagram ?
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Isothermal process - When a thermodynamic system undergoes a thermodynamic process in such a way that its temperature remains constant, then that process is called an Isothermal process.
So, $\mathrm{T}=$ constant and $\Delta T=0$.
Trick to recognize isothermal process -
- The walls of the container must be perfectly conducting (no resistance) which allows the exchange of heat between the gas and surroundings.
- The process of compression or expansion should be infinitely slow so that the process gets proper time for the exchange of heat.
Equation of isothermal process -
As we know that the equation of state is given by $-P V=n R T$
If $\mathrm{T}=$ constant and for a particular amount of gas ' $n$ ' is also constant.
So we can write that - P.V $=$ Constant
Points in graph of isothermal process -
i) Curves obtained on P-V graph are called isotherms and the graphs are hyperbolic in nature.
ii) Slope of isothermal curve :
By differentiating PV = C
$$
\begin{gathered}
P d V+V d P=0 \Rightarrow P d V=-V d P \Rightarrow \frac{d P}{d V}=-\frac{P}{V} \\
\tan \theta=\frac{d P}{d V}=\frac{-P}{V}
\end{gathered}
$$
iii) The area between the isothermal curve and volume axis represents the work done in the isothermal process.
The formula of Work done in the isothermal process -
$$
\begin{aligned}
& W=n R T \log _e\left(\frac{V_f}{V_i}\right)=2.303 n R T \log _{10}\left(\frac{V_f}{V_i}\right) \\
& W=n R T \log _e\left(\frac{P_i}{P_f}\right)=2.303 n R T \log _{10}\left(\frac{P}{P_f}\right)
\end{aligned}
$$
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