Figure shows three isotherms at temperatures 300K, 500K, and 700K, respectively, on PV diagram with broken lines. Three independent thermodynamic process (AB, AC and AD) are performed on 1 mole of monatomic ideal gas as shown in the figure. Then, choose the correct choice(s).

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In the process AC, the temperature of the thermodynamic system is always constant.

In the process AD, average kinetic energy of molecules per unit volume decreases.

In the process AC, first the temperature of the thermodynamic system increases and then decreases.

None of these

answer is B, C.

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Detailed Solution

For process AC;
$p=a-bv [a,b=constant]$
$∴ (a - b v) (v) = R T$
$∴ T = \frac{1}{R} (a v - b v^{2})$
$∴ \frac{d T}{d v} = \frac{a}{R} - \frac{2 b v}{R}$
$0 = \frac{a}{R} - \frac{2 b v}{R} \Rightarrow v = \frac{a}{2 b}$
Also,
${(\frac{d^{2} T}{d v^{2}})}_{\frac{a}{2 b}} < 0$
$∴$ For AC, T first increases andthen decreases.

$F o r A D, T ↓ ∴ K . E ↓$