A fixed mass of a gas is first heated isobarically to double the volume and then cooled isochorically to decrease the temperature back to the initial value. By what factor would the work done by the gas decreased, had the process been isothermal?

Question

A fixed mass of a gas is first heated isobarically to double the volume and then cooled isochorically to decrease the temperature back to the initial value. By what factor would the work done by the gas decreased, had the process been isothermal? (A) 2 (B) (1/2) (C) ln 2 (D) ln3

Tardigrade Admin · Accepted Answer

Δ ( textW) textABC = 2 textP (2 textV - textV) = 2 textPV Δ ( textW) textADC = textnRT text ln ( 2 textV / textV) = 2 textPV ln text2 <img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-bf3dkawrth2pdibb.jpg" /> ∴ The required factor will be = (2 textPV ln 2/2 textPV) = textln 2

Q. A fixed mass of a gas is first heated isobarically to double the volume and then cooled isochorically to decrease the temperature back to the initial value. By what factor would the work done by the gas decreased, had the process been isothermal?

$2$

$\frac{1}{2}$

$l n 2$

$l n 3$

$Δ (W)_{ABC} = 2 P (2 V - V) = 2 PV$
$Δ (W)_{ADC} = nRT ln (2 V / V)$
$= 2 PV ln 2$

$∴$ The required factor will be
$= \frac{2 PV ln 2}{2 PV} = ln 2$

Q. A fixed mass of a gas is first heated isobarically to double the volume and then cooled isochorically to decrease the temperature back to the initial value. By what factor would the work done by the gas decreased, had the process been isothermal?

2

21​

ln2

ln3

Δ(W)ABC​=2P(2V−V)=2PV Δ(W)ADC​=nRT ln(2V/V) =2PV ln2 ∴ The required factor will be =2PV2PV ln2​=ln2

$2$

$\frac{1}{2}$

$l n 2$

$l n 3$

$Δ (W)_{ABC} = 2 P (2 V - V) = 2 PV$
$Δ (W)_{ADC} = nRT ln (2 V / V)$
$= 2 PV ln 2$

$∴$ The required factor will be
$= \frac{2 PV ln 2}{2 PV} = ln 2$