For an ideal gas undergoing an adiabatic process, the equation of state is given as $P T^{- 5 / 2} = k$ , where $k$ is a constant. Find the value of adiabatic index.

\frac{5}{3}

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\frac{7}{5}

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\frac{5}{2}

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Solution

The correct option is A $\frac{5}{3}$
Given,
Equation of state of adiatatic process $P T^{- 5 / 2} = k$
$P^{- 1} T^{5 / 2} = k$
Squaring both sides, $P^{- 2} T^{5} = k$
Taking cube root on both sides, we get
$P^{- 2 / 3} T^{5 / 3} = k$
On comparing with $P^{1 - γ} T^{γ} = k,$ we can conclude that $γ = \frac{5}{3}$

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Thermodynamic Processes

Standard XIII Physics

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For an ideal gas undergoing an adiabatic process, the equation of state is given as PT−5/2=k, where k is a constant. Find the value of adiabatic index.

The correct option is A 53Given, Equation of state of adiatatic process PT−5/2=k P−1T5/2=k Squaring both sides, P−2T5=k Taking cube root on both sides, we get P−2/3T5/3=k On comparing with P1−γTγ=k, we can conclude that γ=53

For an ideal gas undergoing an adiabatic process, the equation of state is given as $P T^{- 5 / 2} = k$ , where $k$ is a constant. Find the value of adiabatic index.