Heat and Thermodynamics 5 Question 29
30. Which one of the following options correctly represents a thermodynamic process that is used as a correction in the determination of the speed of sound in an ideal gas?
(2017 Adv.)
(a) (IV) (ii) (R)
(b) (I) (ii) (Q)
(c) (I), (iv) (Q)
(d) (III) (iv) (R)
Show Answer
Solution:
- $v _{\text {sound }}=\sqrt{\frac{\gamma R T}{M}}$. As the sound wave propagates, the air in a chamber undergoes compression and rarefaction very fastly, hence undergo a adiabatic process. So, curves are steeper than isothermal.
$$ \begin{aligned} \left(\frac{d p}{d V}\right) _{\text {Adi }} & =-\gamma\left(\frac{p}{V}\right) \\ \left(\frac{d p}{d V}\right) _{\text {Iso }} & =-\left(\frac{p}{V}\right) \end{aligned} $$
Graph ’ $Q$ ’ satisfies Eq. (i)
