1 mole of an ideal gas at STP is subjected to a reversible adiabatic expansion to double its volume. The change in internal energy (γ = 1.4)

Question

1 mole of an ideal gas at STP is subjected to a reversible adiabatic expansion to double its volume. The change in internal energy (&gamma; = 1.4)  (A)  1169 J  (B)  769 J  (C)  1373 J  (D)  969 J

Tardigrade Admin · Accepted Answer

For adiabatic expansion T1V1&gamma;-1 =T2V2&gamma;-1 T2 = T1((V1/V2))&gamma;-1 =273 ((1/2))1.4-1 ≃ 206 K dU=dW = (R/&gamma;-1) (T1-T2) =( 1×8.31/(1.4-1))(273-206.89) ≃ 1373 J

Q. $1$ mole of an ideal gas at $STP$ is subjected to a reversible adiabatic expansion to double its volume. The change in internal energy $(γ = 1.4)$

$1169 J$

$769 J$

$1373 J$

$969 J$

For adiabatic expansion
$T_{1} V_{1}^{γ - 1} = T_{2} V_{2}^{γ - 1}$
$T_{2} = T_{1} (\frac{V _{1}}{V _{2}})^{γ - 1} = 273 (\frac{1}{2})^{1.4 - 1}$
$≃ 206 K$
$d U = d W = \frac{R}{γ - 1} (T_{1} - T_{2})$
$= \frac{1 \times 8.31}{( 1.4 - 1 )} (273 - 206.89)$
$≃ 1373 J$

Q. 1 mole of an ideal gas at STP is subjected to a reversible adiabatic expansion to double its volume. The change in internal energy (γ=1.4)

1169J

769J

1373J

969J