Question

Question No. 38


A sample of ideal gas with gamma = 1.5 is compressed from volume of 1600 cc to 400 cc adiabatically. If initial pressure of the gas is 1.5 * 10^5 Pa.
How much internal energy is lost by the gas?

240 J
640 J
370 J
480 J
​

Answer 1

Answer:

480 j

Explanation:

Here,

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<br> In an adiabatic process,

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Answer 2

Given info : A sample of ideal gas with gamma = 1.5 is compressed from volume of 1600 cc to 400 cc adiabatically.

To find : If initial pressure of the gas is 1.5 × 10⁵ Pa, the internal energy lost by the gas is ...

solution : in an adiabatic process,

$PV^{\gamma}=K$

$P_1V_1^{\gamma}=P_2V_2^{\gamma}$

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

and γ = 1.5

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

⇒1.5 × 10⁵ × 64000 = P₂ × 8000

⇒12 × 10⁵ = P₂

q = 0 for adiabatic

so change in internal energy = work done by gas

= $\frac{P_2V_2-P_1V_1}{1-\gamma}$

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

= 6 × 10⁵ × 400 × 10¯⁶ m³/0.5 [ 1cc = 10¯⁶ m³ ]

= 480 J

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

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