The narrow tube with one of its ends sealed as shown in the figure, is in a vertical plane. In the 3 L long horizontal part of the tube, a mercury column of length L blocks some oxygen gas of length L. The outside air pressure of P0 is equal to the pressure of a mercury column of height L. Increasing the temperature of the surrounding, the volume of the blocked gas doubles while the gas absorbs Q=7 J of heat from its surroundings. How much work (in joule) is done by the expanding gas?

Question

The narrow tube with one of its ends sealed as shown in the figure, is in a vertical plane. In the 3 L long horizontal part of the tube, a mercury column of length L blocks some oxygen gas of length L. The outside air pressure of P0 is equal to the pressure of a mercury column of height L. Increasing the temperature of the surrounding, the volume of the blocked gas doubles while the gas absorbs Q=7 J of heat from its surroundings. How much work (in joule) is done by the expanding gas? (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Q=7 J ; Δ Q=Δ U+W ⇒ 7=n Cv Δ T+P d V=n (5/2) R Δ T+n R Δ T 7=(7/2)(n R Δ T) ⇒ n R Δ T=2 J

Q=7J;ΔQ=ΔU+W ⇒7=nCv​ΔT+PdV=n25​RΔT+nRΔT 7=27​(nRΔT) ⇒nRΔT=2J

$Q = 7 J; Δ Q = Δ U + W$
$\Rightarrow 7 = n C_{v} Δ T + P d V = n \frac{5}{2} R Δ T + n R Δ T$
$7 = \frac{7}{2} (n R Δ T)$
$\Rightarrow n R Δ T = 2 J$