The change in internal energy of a given mass of gas, when its volume changes from V to 2V at constant pressure p is( (CP/CV)=γ , universal gas constant =R)

Question

The change in internal energy of a given mass of gas, when its volume changes from V to 2V at constant pressure p is( (CP/CV)=&gamma; , universal gas constant =R) (A)  (pV/&gamma; )  (B)  (pV/(2&gamma; -1))  (C)  (pV/2(&gamma; -1))  (D)  (R/(&gamma; -1))

Tardigrade Admin · Accepted Answer

In case of gases whatever be the process Δ U=nCVΔ T or Δ U=nΔ T( (R/&gamma; -1) ) .. (i) pV=nRT1 2pV=nRT2 ⇒ pV=nR(T2-T1) (pV/R)=nΔ T [T2-T1=Δ T] Substituting in Eq. (i) Δ U=(pV/(&gamma; -1))

Q. The change in internal energy of a given mass of gas, when its volume changes from $V$ to $2 V$ at constant pressure $p$ is( $\frac{C _{P}}{C _{V}} = γ,$ universal gas constant =R)

$\frac{p V}{γ}$

$\frac{p V}{( 2 γ - 1 )}$

$\frac{p V}{2 ( γ - 1 )}$

$\frac{R}{( γ - 1 )}$

$\frac{p V}{( γ - 1 )}$

In case of gases whatever be the process
$Δ U = n C_{V} Δ T$ or $Δ U = n Δ T (\frac{R}{γ - 1})$ .. (i)
$p V = n R T_{1}$
$2 p V = n R T_{2}$
$\Rightarrow$ $p V = n R (T_{2} - T_{1})$
$\frac{p V}{R} = n Δ T$
$[T_{2} - T_{1} = Δ T]$
Substituting in Eq. (i) $Δ U = \frac{p V}{( γ - 1 )}$

Q. The change in internal energy of a given mass of gas, when its volume changes from V to 2V at constant pressure p is( CV​CP​​=γ, universal gas constant =R)

γpV​

(2γ−1)pV​

2(γ−1)pV​

(γ−1)R​

(γ−1)pV​

In case of gases whatever be the process ΔU=nCV​ΔT or ΔU=nΔT(γ−1R​) .. (i) pV=nRT1​ 2pV=nRT2​ ⇒ pV=nR(T2​−T1​) RpV​=nΔT [T2​−T1​=ΔT] Substituting in Eq. (i) ΔU=(γ−1)pV​