First slide

Different type of processes

Question

During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its temperature. The ratio of $\frac{C_{p}}{C_{υ}}$ for the gas is

Moderate

A

$\frac{5}{3}$
B

$\frac{3}{2}$
C

$\frac{4}{3}$
D

$2$

Solution

$P \propto T^{3}$
$P T^{3}$ = constant ---(i)
For an adiabatic process,
$P T^{γ / 1 - γ}$ =constant ---(ii)
Comparing (i) and (ii), we get
$\frac{γ}{1 - γ} = - 3 γ = - 3 + 3 γ - 2 γ = - 3 o r γ = \frac{3}{2} A s γ = \frac{C_{p}}{C_{υ}} ∴ \frac{C_{p}}{C_{υ}} = \frac{3}{2}$

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