Assertion : The isothermal curves intersect each other at a certa… - Vidyadip

Question

$Assertion :$ The isothermal curves intersect each other at a certain point.
$Reason :$ The isothermal change takes place slowly, so, the isothermal curves have very little slope.

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Answer

Isothermal curves have slope which is equal to $\frac{P}{V}$. It can be calculated as follows $PV = RT$ Differentiating, $PdV + VdP = 0$ $-\frac{dP}{dV} = \frac{P}{V}$ Now, if they cut each other at certain point, they will have different slope at the same point (for same value of $P$ and $V$). So, they can not cut each other at some point. Reason is true, slope is $\frac{P}{V}$ . For adiabatic curve slope is $\gamma $ times $\frac {P}{V}$ .

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