Fixed mass of a triatomic non-linear ideal gas is subjected to the changes as shown in diagram, calculate T3, P2 and V2 as shown in diagram. Consider vibrational degree is to be inactive and gas obeys PV = nRT equation. [Fill your answer as T3 (K)+ P2 (atm)+ V2(L)]

Engineering

Chemistry

First Law and Various Process

Question

Fixed mass of a triatomic non-linear ideal gas is subjected to the changes as shown in diagram, calculate T₃, P₂ and V₂ as shown in diagram. Consider vibrational degree is to be inactive and gas obeys PV = nRT equation. [Fill your answer as T₃(K)+ P₂ (atm)+ V₂(L)]

LiveFree JEE Main Previous Year Online Papers Live Free JEE Advance Previous Year Online Papers

College PredictorLive

Know your College Admission Chances Based on your Rank/Percentile, Category and Home State.

Get your JEE Main Personalised Report with Top Predicted Colleges in JoSA

For triatomic non-linear gas,
C_V = $\frac{3 R}{2} + \frac{3 R}{2} = \frac{6 R}{2}$
C_P = $\frac{8 R}{R}$ ⇒ γ = $\frac{C_{P}}{C_{V}} = \frac{8}{6} = \frac{4}{3}$
T₁ = T₂ = 400 K (Since PV = constant)
When volume is constant
$\frac{P_{3}}{T_{3}} = \frac{P_{2}}{T_{1}}$
$\Rightarrow \frac{16}{T_{3}} = \frac{P_{2}}{400}$ ....(i)
When PV = constant
P₂ × 1 L = P₁ × V₂
⇒ P₂ × 1 L = 1 atm × V₂ ....(ii)
When PV^γ = constant
P₃ × 1^γ = P₁ × V₂^γ

⇒ P₃ = V₂^4/3 (γ = 4/3)
⇒ 16 = V₂^4/3
⇒ V₂ = 8 L
$∴$ P₂ = 8 atm
and T₃ = $\frac{16 \times 400}{8}$ = 800 K
8008.08

Please subscribe our Youtube channel to unlock this solution.