Question

A sample of ideal gas with y = 1.5 is compressed
from volume of 1600 cc to 400 cc adiabatically. If
initial pressure of the gas is 1.5x 105 Pa. How much
internal energy is lost by the gas?
•240 J
•640 J
•370 J
•480 J​

Answer 1

ARE YOU FAILURE???

@MR.RANDOM

Answer 2

Given info : A sample of ideal gas with y = 1.5 is compressed from volume of 1600 cc to 400 cc adiabatically. If initial pressure of the gas is 1.5 x 105 Pa.

To find : The internal energy lost by the gas is ...

solution : for adiabatic process,

$PV^{\gamma}=K$

i.e., $P_1V_1^{\gamma}=P_2V_2^{\gamma}$

here, P₁ = 1.5 × 10⁵Pa , V₁ = 1600 cc , V₂ = 400 cc and P₂ = ?

∴ 1.5 × 10⁵ × (1600)^(3/2) = P₂ × (400)^(3/2)

⇒1.5 × 10⁵ × 64000 = P₂ × 8000

⇒P₂ = 12 × 10⁵ Pa

now change in internal energy = work done by the gas

= (P₁V₁ - P₂V₂)/(γ - 1)

= (1600cc × 1.5 × 10⁵ Pa - 400cc × 12 × 10⁵ Pa)/(1.5 - 1)

= (1600 × 10¯⁶ m³ × 1.5 × 10⁵ Pa - 400 × 10¯⁶ m³ × 12 × 10⁵ Pa)/(1.5 - 1)

= (240 - 480)/(0.5)

= -480 J

Therefore the internal energy lost by the gas is 480 J.

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