Question

1 mm³ Of a gas is compressed at 1 atmospheric pressure and temperature 27^o C to 627^o C What is the final pressure under adiabatic condition. r = 1.5 

(A) 80 × 10⁵ (N / m²) 

(B) 36 × 10⁵ (N / m²) 

(C) 56 × 10⁵ (N / m²) 

(D) 27 × 10⁵ (N / m²)

Answer 1

Correct option: (D) 27 × 10⁵ (N / m²)

Explanation:

V₁ = 1mm³ 

P₁ = 1 atm = 10⁵ N/m² 

T₁ = 27 °C = 300 K

T₂ = 627 °C = 900 K

γ = 1.5

Under adiabatic condition,

(T₁ / T₂) = (P₁ / P₂)^{[(γ–1) / γ]} 

∴  [(300) / (900)] = (10⁵ / P₂)^{[(1.5 – 1) / 1.5]} 

∴   (1/3) = (10⁵ / P₂)^1/3 

∴  (1/3)³ = (10⁵ / P₂)

∴  P₂ = 27 × 10⁵ N/m²