Question

An ideal gas in a balloon is kept in thermal equilibrium with its constant-temperature surroundings. How much work is done if the outside pressure is slowly reduced, allowing the balloon to expand to 50 times its original size

Answer 1

w = 252.32 N

Step-by-step explanation:

given data

balloon expand = 50 times its original size

we consider here initially pressure and volume

pressure = 645 pa

volume = 0.10 m³

solution

as in isothermala process ideal gas

PV = mRT

P =
`(mRT)/(v)`

P =
`(c)/(v)`

here c is constant

so work done is express as

`w = c \int\limits^(V2)_(V1) {(dv)/(v)}`

w =
`c * ln( (v2)/(v1))`

and we know c = p1 × v1

so

w = p1 × v1 ×
`ln ((50v1)/(v1) )`

w = 645 × 0.1 × ln(50)

w = 252.32 N