Question

One mole of an ideal gas is initially kept in a cylinder with a movable frictionless and massless piston at pressure of 1.01 M Pa, and temperature 27°C. It is then expanded till its volume is doubled. How much work is done if the expansion is isobaric?

Answer 1

Given:

n = 1 mole

P = 1.01 M Pa = 1.01 × 10⁶ Pa

T_i = 27 C = 27 + 273 = 300 K

V_f = 2 V_i

To find:

Wok done (W) = ?

Formula:

1. W = PΔV
2. PV_i = nRT

Solution:

PV_i = nRT_i

∴ V_i = `(nRT_i)/(P)`

= `(1 xx 8.31 xx 300)/(1.01 xx 10^6)`

= `(24.93)/(1.01 xx 10^6)`

= 24.93 × 10⁻⁴ m³

∴ W = P(V_f – V_i)

= P(2V_i – V_i)

= PVi

= 1.0 × 10⁶ × 24.93 × 10^–4

= 1 × 24.93 × 10² T

∴ W = 2.493 × 10³ J