Question

An ideal gas expands isothermally and reversibly from 10 m³ to 20 m³ at 300 K performing 5 .187 kJ of work on surrounding. Calculate number of moles of gas undergoing expansion. (R = 8.314 J K^-1 mol^-1)

Options

• 2

• 3

• 1.5

• 1

Answer 1

3

Explanation:

V₁ = 10 m³, V₂ = 20 m³, T = 300 K

W_max = - 5.187 kJ = - 5187 J, n = ?

W_max = - 2.303 nRT `log_10  "V"_2/"V"_1`

∴ - 5187 = - 2.303 × n × 8.314 × 300 `log_10  20/10`

∴ n = `5187/(2.303 xx 8.314 xx 300 xx log_10 2)`

`= 5187/(2.303 xx 8.314 xx 300 xx 0.3010)`

∴ n = 3 mol