A certain mass of a gas was heated in a constant volume vessel, its P-T curve is 1, similarly alnother mass of the gas was heated in the same vessel , its P-T curve is 2. if tan `beta=2` tan `alpha` what is the ratio of masses of gas in the two experiments?

Explanation

From ideal gas equation,
`P=((nR)/(V))T = ((mR)/(MV))T`
The constant volume curves are strainght lines with slope `mR//MV`. The slope of lines is proportional to the mass of the gas.
From ideal gas equation.
`P=((nR)/V)T = ((mR)/(MV))T`
The constant volume curves are straight line with slope mR//MV.The slope of line is propotional to the mass of the gas.
`((slope)_(1))/((slope)_(2))=(m_(1))/(m_(2))=(tanalpha)/(tanbeta)=1/2 `
`Hence the mass M_(2) is twice of m_(1)`