Question

A cylinder with a moving piston expands from an initial volume of 0.350 L against an external pressure of 1.90 atm. The expansion does 287 J of work on the surroundings. What is the final volume of the cylinder

Answer 1

1.84 L

Step-by-step explanation:

Using the equation for reversible work:

`W = -P*(V_(2) - V_(1))`

Where:

W is the work done (J) = -287 J.

Since the gas did work, therefore W is negative.

P is the pressure in atm = 1.90 atm.

However, work done is in joules and pressure is in atm. We can use the values of universal gas constant as a convenient conversion unit. R = 8.314 J/(mol*K); R = 0.0821 (L*atm)/(mol*K)

Therefore, the conversion unit is 0.0821/8.314 = 0.00987 (L*atm)/J

`V_(1)` is the initial volume = 0.350 L

`V_(2)` is the final volume = ?

Thus:

(-287 J)*0.00987 (L*atm)/J = -1.9 atm*(
`V_(2)` - 0.350) L

`V_(2)` = [(287*0.00987)+(1.9*0.350)]/1.9 = (2.833+0.665)/1.9 =1.84 L