SATHEE: Heat and Thermodynamics 6 Question 2

Heat and Thermodynamics 6 Question 2

6. Consider an ideal gas confined in an isolated closed chamber. As the gas undergoes an adiabatic expansion, the average time of collision between molecules increases as $V^{q}$ , where $V$ is the volume of the gas. The value of $q$ is $(γ = \frac{C_{p}}{C_{V}})$

(a) $\frac{3 γ + 5}{6}$

(b) $\frac{γ + 1}{2}$

(d) $\frac{γ - 1}{2}$

(2015 Main)

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Answer:

Correct Answer: 6. (b)

Solution:

Average time between two collisions is given by

$τ = \frac{1}{\sqrt{2} π n v_{r m s} d^{2}}$

Here, $n =$ number of molecules per unit volume $= \frac{N}{V}$

and $v_{r m s} = \sqrt{\frac{3 R T}{M}}$

Substituting these values in Eq.(i) we have,

$τ \propto \frac{V}{\sqrt{T}}$

For adiabatic process, $T V^{γ - 1} =$ constant

substituting in Eq. (ii), we have $τ \propto \frac{V}{\sqrt{(\frac{1}{V^{γ - 1}})}}$

$τ \propto V$ or $τ \propto V^{(2})$

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Heat and Thermodynamics 6 Question 2

6. Consider an ideal gas confined in an isolated closed chamber. As the gas undergoes an adiabatic expansion, the average time of collision between molecules increases as Vq, where V is the volume of the gas. The value of q is (γ=CpCV)

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6. Consider an ideal gas confined in an isolated closed chamber. As the gas undergoes an adiabatic expansion, the average time of collision between molecules increases as $V^{q}$ , where $V$ is the volume of the gas. The value of $q$ is $(γ = \frac{C_{p}}{C_{V}})$