An ideal gas of molecular mass M is located in the uniform gravitational field in which the free-fall acceleration is g. Find the gas pressure as a function of height h, if P is equal P_(0) at h = 0 and the temperature varies with has T=T_(0) (1-ah). where a is a positive constant.

An ideal gas of molecular mass M is located in the uniform gravitation

1.	An ideal gas of molecular mass M is located in the uniform gravitational field in which the free-fall acceleration is g. Find the gas pressure as a function of height h, if P is equal P_(0) at h = 0 and the temperature varies with has T=T_(0) (1-ah). where a is a positive constant.
Answer» Solution :We have shown that, `(dP)/P=-(Mg)/(RT)dh` GIVEN `T=T_(0)(1-ah)` `therefore (dP)/P=(Mg)/(RT_(0)(1-ah))dh` Integrating on both SIDES, we GET `int_(po)^(p)(dP)/P=-(Mg)/(RT_(0))int_(0)^(h)(dh)/(1-ah)` `log_(e)(P//P_(0))=-(Mg)/(RT_(0))(log_(e)(1-ah))/((-a))" (or) "log_(e)(P//P_(0))=log_(e)(1-ah)^(n)` where `n=(Mg)/(aRT_(0))" (or) "P/P_(0)=(1-ah)^(n)" (or) "P=P_(0)(1-ah)^(n)=P_(0)(1-ah)^(("RG")/("aRT"))`