Prove that V= sqrt( gamma CT) from the ideal gas equation for speed of

1.	Prove that V= sqrt( gamma CT) from the ideal gas equation for speed of sound is gases.
Answer» Solution :Let us consider an IDEAL GAS whose equation of state is `PV= nRT "" ...(1)` where P-pressure, V- volume, T-temperature, n-number of mole and R-universal gas CONTANT. For a GIVEN mass of molecules equation (1) can be written as `(PV)/(T)` constant `""...(2)` for a fixed mass m, density of the gas inversely varies with volume i.e., `rho prop (1)/(V),V=(m)/(rho) ""....(3)` Substituting equation (3) in equation (2), we get `(P)/(rho)=cT ""...(3)` where c proportionality is constant. `:. v=sqrt((gamma P)/(rho))= sqrt(gamma cT)`

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