First slide

Different type of processes

Question

In adiabatic process $R = \frac{2}{3} C_{V}$ . The pressure of the gas will be proportional to

Moderate

A

$T^{\frac{5}{2}}$
B

$T^{\frac{5}{3}}$
C

$T^{\frac{5}{6}}$
D

$T^{\frac{5}{4}}$

Solution

$C_{P} - C_{V} = R \Rightarrow C_{P} - C_{V} = \frac{2}{3} C_{V} \Rightarrow \frac{C_{P}}{C_{V}} = γ = \frac{5}{3}$
Now $p α {(T)}^{\frac{γ}{(γ - 1)}} \Rightarrow p α {(T)}^{\frac{5 / 3}{(\frac{5}{3} - 1)}} \Rightarrow p α T^{\frac{5}{2}}$

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