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Work Done in Isothermal Reversible Process

Two different...

Question

Two different adiabatic paths for the same gas intersects two isothermals at $T_{1}$ and $T_{2}$ as shown in $P - V$ diagram. find out the ratio of $\frac{V_{a}}{V_{d}}$ and compare with ratio $\frac{V_{b}}{V_{c}}$ ?

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Solution

As per Isotropic process,
$\frac{T_{e}}{T_{B}} == {(\frac{V_{B}}{V_{C}})}^{γ - 1}$ and $\frac{T_{D}}{T_{A}} = {(\frac{V_{A}}{V_{D}})}^{γ - 1}$
Now, $T_{C} = T_{D}$ and $T_{B} = T_{A}$
$\frac{V_{B}}{V_{C}} = \frac{V_{A}}{V_{D}} = r$
where $r$ is the compression or expansion ratio.

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