Question

one mole of an ideal gases expands isothermally to five times to its intial volume calculate entropy change in terms of R the gas constant

Answer 1

isothermal process ,

so, dT = 0

we know,
entropy = heat/temperature

dQ = dU + dW
but in isothermal dU = 0
so , dQ = dW
dQ = dW =pdV
we know,

PV = nRT
P = nRT/V
so, PdV = nRTdV/V

use this in entropy ,

now, entropy = nRTdV/VT
=nR{ dV/V}
=nR ln[V]
=nRlnVf/Vi
where Vf is final volume and Vi is initial volume .
now,
given,
n = 1
Vi = V
Vf = 5V

so, entropy = 1 × R ln5V/V = Rln5

so, entropy = Rln5