50.65J
The P-V work done by a gas on its surrounding at constant pressure is given by;
W = | -PΔV | --------------------------------(i)
Where;
P = Pressure of the gas
ΔV = Change in the volume of the gas = final volume of the gas(V₂) - initial volume of the gas(V₁)
i.e
ΔV = V₂ - V₁
Therefore, equation (i) could be re-written as;
W = P (V₂ - V₁) --------------------(ii)
From the question;
V₂ = 750mL
V₁ = 250mL
P = 1.00atm
Substitute these values into equation(ii) as follows;
W = 1.00 (750 - 250)
W = 1.00(500)
W = 500 atm.mL
Convert the result to Joules as follows;
(i) first convert to atm.L;
500 atm. mL = 500 atm.mL x 10⁻³L / mL = 0.5atm.L
(ii) then convert to Pa.L
0.5atm.L = 0.5 atm.L x 1.013 x 10⁵Pa / atm = 0.5065 x 10⁵Pa L
(ii) now convert to Pa.m³ (which is equivalent to 1 Joule)
0.5065 x 10⁵Pa.L = 0.5065 x 10⁵ Pa.L x m³ / 1000L = 50.65 Pa.m³
Therefore, the work done is 50.65J
We have that the is mathematically given as
From the question we are told
Generally the equation for the workdone is mathematically given as
[tex]W=PdV\\\\Therefore\\\\w=1*500\\\\w=0.500Latm[/tex]
Therefore
w in J
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