Show that Laplace correction for elasticity of gaseous medium is E = gamma p, where 'gamma' is the ratio of specific heates.

Show that Laplace correction for elasticity of gaseous medium is E = g

1.	Show that Laplace correction for elasticity of gaseous medium is E = gamma p, where 'gamma' is the ratio of specific heates.
Answer» <html><body><p></p>Solution :Consider adiabatic variation in the <a href="https://interviewquestions.tuteehub.com/tag/pressure-1164240" style="font-weight:bold;" target="_blank" title="Click to know more about PRESSURE">PRESSURE</a> and volume of gasesousmedium. <br/> `<a href="https://interviewquestions.tuteehub.com/tag/pv-593601" style="font-weight:bold;" target="_blank" title="Click to know more about PV">PV</a>^(gamma) =0 ` <br/> i.e., `gamma PV^(gamma-<a href="https://interviewquestions.tuteehub.com/tag/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</a>) Dleta V + V^(gamma) Delta P = 0` <br/> i.e., Bulk modulus-`( Delta P )/((DeltaV)/( V)) = gamma P` <br/> Hence in the expression`v = sqrt((E )/(rho ))`, Elasticity 'E' is replaced by `gamma P`. <br/> <a href="https://interviewquestions.tuteehub.com/tag/laplace-539362" style="font-weight:bold;" target="_blank" title="Click to know more about LAPLACE">LAPLACE</a> equation is written as `v =sqrt((gamma P )/( rho ))` <br/> Where `gamma = 1+ 2 //f` and'f' is number of degrees of freedom of gaseous molecule.</body></html>