Physics Olympiad USA Math Olympiad

Specific Heat of a Rigid Triangular Molecule

A rigid triangular molecule consists of three non-collinear atoms joined by rigid rods. The constant pressure molar specific heat \(C_p\) of an ideal gas consisting of such molecules is

(a) \(6R\)

(b) \(5R\)

(c) \(4R\)

(d) \(3R\)

Degrees of freedom are the number of independent parameters that define its configuration
If \(N\) be the number of particles in a system and \(k\) be the number of constraints between the number of degrees of freedom is given by $$ f=3N-k$$ $$f=(3*3)-3$$ $$=6$$
Relation between \(f\) and \(C_p\) $$ C_p=(f/2+1)R$$ $$ \Rightarrow C_p=(6/2+1)R$$ $$C_p=4R$$

By Ashani Dasgupta

Ph.D. in Mathematics from University of Wisconsin Milwaukee (USA)
Founder - Faculty at Cheenta

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