IF `pv^gamma=c` [`gamma` and c are constants], show that,
`v^2(d^2p)/(dv^2)=gamma(gamma+1)p`

pv^a=c (a and c are constants) then show that v^2(d^2p)/(dv^2)=a(a+1)p .

If pv^(a)=c (a and c are costants) then show that v^(2)(d^(2)p)/(dv^(2))=a(a+1)p

The relation between internal energy U, pressure p and volume V of a gas in an adiabatic process is : U = a + bpV where a and b are constants. If the ratio of c_(p) and c_(v) of the gas is gamma , prove that, gamma = (b+1)/(b) .

if alpha , beta , gamma are in A>P show that cot =(sinalpha-singamma)/(cosgammacosalpha)

If alpha,beta,gamma are in A.P. show that cot beta=(sin alpha-sin gamma)/(cos gamma-cos alpha)

If alpha,beta,gamma "are in A.P. show that" cot beta = (sin alpha - sin gamma)/(cos gamma -cos alpha)

If cos alpha+ cos beta+ cos gamma + cos alpha cos beta cos gamma=0 , show that sin alpha (1+ cos beta cos gamma)=+- sin beta sin gamma .

If sec alpha = sec beta sec gamma+ tan beta tan gamma , then show that sec beta= sec gamma sec alpha+- tan gamma tan alpha .

Prove that pV ^(gamma ) = constant in adiabatic process .

If alpha,beta,gamma are different from 1 and are the roots of a x^3+b x^2+c x+d=0a n d(beta-gamma)(gamma-alpha)(alpha-beta)=(25)/2 , then prove that |alpha/(1-alpha)beta/(1-beta)gamma/(1-gamma)alphabetagammaalpha^2beta^2gamma^2|=(25 d)/(2(a+b+c+d))