Question

Two mole of a monoatomic ideal gas is expanded
irreversibly and isothermally at T Kelvin until its volume
is doubled and q joules heat is absorbed from surrounding.
S (J/K) (system + surrounding) is :
(a) zero
(b) 2 Rln2–q/T
(C) 3Rln2–q/T
(d)-2 Rln2+q/T​

Answer 1

Answer:

Given that n=2

T=T Kelvin

$V_{1} =V  and V_{2} =2V$

q=q joules

Δ$S_{surr}= \frac{-q}{T}$

Δ$S_{sys} =C_{V} ln\frac{T_{2} }{T_{1} } +R ln \frac{V_{2} }{V_{1} }$

dq=dV+pdV

dq=$nC_{V} dT$+$\frac{nRT}{V} dV$

dS=$\frac{dq}{T}$

dS=$\frac{nC_{V} dT}{T} +\frac{nRdV}{V}$

ΔS=$nC_{V} \int\limits^T_T _\frac{dT}{T}$+$nR\int\limits^V_V\frac{dv}{v}$

ΔS=$nC_{V} ln\frac{T_{2} }{T_{1} } +nRln\frac{V_{2} }{V_{1} }$

Here finally we got

Δ$S_{sys} =nRln\frac{V_{2} }{V_{1} }$

so we get ΔS(system+surrounding)=

                                 $2Rln2-q/T$

option b is correct