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

Answer:

w = 252.32 N

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 = $\frac{mRT}{v}$

P = $\frac{c}{v}$

here c is constant

so work done is express as

$w = c \int\limits^{V2}_{V1} {\frac{dv}{v}}$  

w = $c \times ln( \frac{v2}{v1})$

and we know c  = p1 × v1

so

w = p1 × v1 × $ln (\frac{50v1}{v1} )$

w = 645 × 0.1 × ln(50)

w = 252.32 N