What is the change in internal energy of one mole of a gas, when volume changes from V to 2V at constant pressure P?

Question

What is the change in internal energy of one mole of a gas, when volume changes from V to 2V at constant pressure P? (A) (R/(&gamma;-1)) (B) PV (C) (PV/(&gamma;-1)) (D) (&gamma; PV/(&gamma;-1))

Tardigrade Admin · Accepted Answer

According to ideal gas equation, PV = nRT When pressure is constant, PdV = nRdT P(2V - V) = nRdT PV = nRdT ...(i) As &gamma;=(CP/CV) ∴ &gamma;-1=(CP-CV/CV) or CV=(CP-CV/&gamma;-1)=(R/&gamma;-1) (∵ CP-CV=R) Δ u=(PV/&gamma;-1) (Using (i))

Q. What is the change in internal energy of one mole of a gas, when volume changes from $V$ to $2 V$ at constant pressure $P$ ?

$\frac{R}{( γ - 1 )}$

$P V$

$\frac{P V}{( γ - 1 )}$

$\frac{γ P V}{( γ - 1 )}$

Q. What is the change in internal energy of one mole of a gas, when volume changes from V to 2V at constant pressure P?

(γ−1)R​

PV

(γ−1)PV​

(γ−1)γPV​

According to ideal gas equation, PV=nRT When pressure is constant, PdV=nRdT P(2V−V)=nRdT PV=nRdT...(i) As γ=CV​CP​​ ∴γ−1=CV​CP​−CV​​ or CV​=γ−1CP​−CV​​=γ−1R​(∵CP​−CV​=R) Δu=γ−1PV​ (Using (i))

Q. What is the change in internal energy of one mole of a gas, when volume changes from $V$ to $2 V$ at constant pressure $P$ ?

$\frac{R}{( γ - 1 )}$

$P V$

$\frac{P V}{( γ - 1 )}$

$\frac{γ P V}{( γ - 1 )}$