If the ratio of specific heat of a gas at constant pressure to that at the constant volume is γ , the change in internal energy of the mass of gas, when the volume changes from V to 2V at constant pressure p, is

Question

If the ratio of specific heat of a gas at constant pressure to that at the constant volume is &gamma; , the change in internal energy of the mass of gas, when the volume changes from V to 2V at constant pressure p, is (A)  textR / (&gamma; - 1) (B)  textpV (C)  textpV / (&gamma; - 1) (D) &gamma; textpV / (&gamma; - 1)

Tardigrade Admin · Accepted Answer

Δ U = n C v Δ T Also, ( C p / C v )=&gamma; Hence ( C p - C v / C v )=&gamma;-1 ⇒ C v = R /(&gamma;-1) Δ U =( nR /&gamma;-1) Δ T =( p Δ V /&gamma;-1)=( p (2 V - V )/&gamma;-1)=( pV /&gamma;-1)

Q. If the ratio of specific heat of a gas at constant pressure to that at the constant volume is $γ$ , the change in internal energy of the mass of gas, when the volume changes from V to 2V at constant pressure p, is

$R / (γ - 1)$

$pV$

$pV / (γ - 1)$

$γ pV / (γ - 1)$

$Δ U = n C_{v} Δ T$
Also, $\frac{C _{p}}{C _{v}} = γ$
Hence $\frac{C _{p} - C _{v}}{C _{v}} = γ - 1$
$\Rightarrow C_{v} = R / (γ - 1)$
$Δ U = \frac{n R}{γ - 1} Δ T = \frac{p Δ V}{γ - 1} = \frac{p ( 2 V - V )}{γ - 1} = \frac{p V}{γ - 1}$

Q. If the ratio of specific heat of a gas at constant pressure to that at the constant volume is γ , the change in internal energy of the mass of gas, when the volume changes from V to 2V at constant pressure p, is

R/(γ−1)

pV

pV/(γ−1)

γpV/(γ−1)