A sample of gas occupies a volume of 54.0 mL. As it expands, it does 137.1 J of work on its surroundings at a constant pressure of 783 torr. What is the final volume of the gas?
The relation between Pressure, Work and Volume is given by,
Where deltaV = Vfinal - Vinitial
Negative sign will be used for work as it is done by the system since the gas is expanding.
We will change the values into requisite unit so that Volume can be obtained in L.
w =137.1J = 137.1/101.3L.atm = 1.353L.atm (1L.atm=101.3J)
w = -1.353L.atm
P = 783 torr = 783/760atm = 1.03atm (1 atm = 760torr)
-1.353L.atm = -1.03atm.deltaV
DeltaV = 1.31L
Vfinal - Vinitial = 1.31L
Vinitial = 54mL = 0.054L
Vfinal = 1.31L + 0.054L = 1.364L = 1364mL
Final volume = 1364mL
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