Question

Air is compressed in a cylinder such that the volume changes from 100.0 to 10.0 in^3. The initial pressure is 50.0 psia and the temperature is held at a constant 100.0 °F. How much work is required to change the volume? (Hint you will need to identify what psia means)

Answer 1

5953.42 J

Step-by-step explanation:

Given:

Initial volume,
`V_i`= 100 in³

Final Volume,
`V_f` = 10 in³

Initial pressure = 50 psia

Temperature = 100° F = 310.93 K

For isothermal reversible process, work done is given as:

Work done =
`-2.303RTlog_(10)(V_f)/(V_i)`

Where,

R is the ideal gas constant = 8.314 J/mol.K

or

Work done =
`-2.303*8.314*310.93log_(10)(10)/(100)`

or

Work done = 5953.42 J