1 mole of NH 3 gas at 27° C is expanded in reversible adiabatic condition to make volume 8 times (γ=1.33). Final temperature and work done respectively are :

Question

1 mole of NH 3 gas at 27° C is expanded in reversible adiabatic condition to make volume 8 times (&gamma;=1.33). Final temperature and work done respectively are : (A) 150 K , 900 cal (B) 150 K , 400 cal (C) 250 K , 1000 cal (D) 200 K , 800 cal

Tardigrade Admin · Accepted Answer

T1 V1&gamma;-1=T2 V2&gamma;-1 ⇒ 300 × V1 / 3 =T2(8 V)1 / 3 ⇒ T2=150 K W=n Cv(T2-T1)=1 × 3 R(150-300) =3 × 2(-150)=-900 ca

Q. $1$ mole of $N H_{3}$ gas at $2 7^{\circ} C$ is expanded in reversible adiabatic condition to make volume $8$ times $(γ = 1.33)$ . Final temperature and work done respectively are :

150 K , 900 cal

150 K , 400 cal

250 K , 1000 cal

200 K , 800 cal

$T_{1} V_{1}^{γ - 1} = T_{2} V_{2}^{γ - 1} \Rightarrow 300 \times V^{1/3}$
$= T_{2} (8 V)^{1/3} \Rightarrow T_{2} = 150 K$
$W = n C_{v} (T_{2} - T_{1}) = 1 \times 3 R (150 - 300)$
$= 3 \times 2 (- 150) = - 900 c a$

Q. 1 mole of NH3​ gas at 27∘C is expanded in reversible adiabatic condition to make volume 8 times (γ=1.33). Final temperature and work done respectively are :