Question

For the isothermal expansion of one mole of an ideal gas from 1dm3 to 4 dm3, at 27c the value of ∆U is

Answer 1

∆U is change in internal energy of ideal gas. we know, internal energy of an ideal gas depends on temperature. in case of isothermal process, temperature remains constant. so, internal energy also remains same. so, change in internal energy , ∆U = 0.

but workdone , w = $-nRTln\left[\frac{V_f}{V_i}\right]$

here, n = 1, R = 25/3 J/mol.K, T = 27°C = 273 + 27= 300K and volume increases from 1dm³ to 4dm³.

then, w = -1 × 25/3 × 300 × ln(4/1)

= -2500ln(4)

= -500ln2 Joule

= -346.57 J