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 used.

Options

• 1.5

• 1

• 3

• 2

Answer 1

3

Explanation:

W = `- int "p"."dV"`

Substituting the ideal gas equation for pleads to,

W = `- int "nRT"/"V"."dV"`

Since the process is isothermal,

W = `- "nRT In" ("V"_2/"V"_1)`

`- 5.187 xx 1000  "J" = - "n" xx 8.314  "JK"^-1  "mol"^-1  "In" ((20  "m"^3)/(10  "m"^3))`

n = `(5.187 xx 1000)/(8.314 xx "In"  2)` mol

= `(5.187 xx 1000)/(8.314 xx 0.6931)` mol

= 3 mol