An ideal gas is compressed at constant pressure to one-half itsinitial volume. I

Question

An ideal gas is compressed at constant pressure to one-half itsinitial volume. If the pressure of the gas is 120 kPa, and790 J of work is done on it, find the initial volume of the gas.
1/2Vi=Vf P= constant= 120 kPa= 120000 Pa W= 790 J W= P(Vf - Vi) W=P(1/2Vi - Vi) W - P= Vi(1/2 - 1) (W - P)/(1/2 - 1)= Vi -2(W - P)= Vi -2(790 - 120000)= Vi= 238420 m3





1/2Vi=Vf P= constant= 120 kPa= 120000 Pa W= 790 J W= P(Vf - Vi) W=P(1/2Vi - Vi) W - P= Vi(1/2 - 1) (W - P)/(1/2 - 1)= Vi -2(W - P)= Vi -2(790 - 120000)= Vi= 238420 m3

Explanation / Answer

1/2Vi=Vf      -
P= constant= 120 kPa= 120000 Pa  
W= 790 J
W= P(Vf - Vi)    -----wrong, work done ON the gas W = P(Vi -Vf)
W = P(Vi - Vi/2) W/P= Vi(1 -1/2)                not W - P = ...
W/P = Vi/2
Vi = 2W/P = 0.0132 m3

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