A diatomic gas is heated at constant pressure. What fraction of the heat energy is used to increase the internal energy?

Question

A diatomic gas is heated at constant pressure. What fraction of the heat energy is used to increase the internal energy? (A)  (3/5)  (B)  (3/7)  (C)  (5/7)  (D)  (5/9)

Tardigrade Admin · Accepted Answer

Fraction of supplied energy which increases the internal energy is given by f =(Δ U/(Δ Qp))=((Δ Q)V/(Δ Qp)p) =(μ CV Δ T/μ Cp Δ T)=(1/&gamma;) For diatomic gas &gamma;=(7/5) ⇒ f=(5/7)

Q. A diatomic gas is heated at constant pressure. What fraction of the heat energy is used to increase the internal energy?

$\frac{3}{5}$

$\frac{3}{7}$

$\frac{5}{7}$

$\frac{5}{9}$

Fraction of supplied energy which increases the internal energy is given by
$f = \frac{Δ U}{( Δ Q _{p} )} = \frac{( Δ Q ) _{V}}{( Δ Q _{p} ) _{p}}$
$= \frac{μ C _{V} Δ T}{μ C _{p} Δ T} = \frac{1}{γ}$
For diatomic gas $γ = \frac{7}{5}$
$\Rightarrow f = \frac{5}{7}$