The equation of state for a gas is given by PV = nRT + α V, where n is the number of moles and a is a positive constant. The initial temperature and pressure of one mole of the gas contained in a cylinder are To and Po respectively. The work done by the gas when its temperature doubles isobarically will be :

Question

The equation of state for a gas is given by PV = nRT + α V, where n is the number of moles and a is a positive constant. The initial temperature and pressure of one mole of the gas contained in a cylinder are To and Po respectively. The work done by the gas when its temperature doubles isobarically will be : (A) (PO TOR/PO -α) (B) (PO TOR/PO +α) (C) PO TOR ℓ n 2 (D) PO TOR

Tardigrade Admin · Accepted Answer

P0V0=nRT0 P0V0=nRT Tf =2T0 W=∫ PdV =∫ ((nRT/V)+α)dv PV=nRT+α V ∫ pdV=∫ limits2T0T0nRdT+∫ limitsVfViα dV =nRT0+ α Vi =nRT0+α((nRT0/P0)) =nRT0(1+(α/P0)) PV = nRT + α V ∫ pdV=∫ nRdT+∫α dV W=nRT0+α[(nRT0/P0-α)] W=nRT0[1+(α/p0-α)] =nR0T0[(P0/P0-α)] =(nRT0 P0/P0-α)

$\frac{P _{O} T _{O} R}{P _{O} - α}$

$\frac{P _{O} T _{O} R}{P _{O} + α}$

$P_{O} T_{O} R ℓ n 2$

$P_{O} T_{O} R$

PO​−αPO​TO​R​

PO​+αPO​TO​R​

PO​TO​Rℓn2

PO​TO​R

$\frac{P _{O} T _{O} R}{P _{O} - α}$

$\frac{P _{O} T _{O} R}{P _{O} + α}$

$P_{O} T_{O} R ℓ n 2$

$P_{O} T_{O} R$