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Heat and Thermodynamics question

2010 · Q90
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Heat and Thermodynamics question

2010 · Q90

NEETPhysicsHeat and ThermodynamicsMCQ+4 / −1
A monatomic gas at pressure P1 and volume V1 is compressed adiabatically to 18th{{1 \over 8}^{th}}81​th of its original volume. What is the final pressure of the gas?
  1. A
    64P1
  2. B
    P1
  3. C
    16P1
  4. D
    32P1
View written solutionFree

Correct answer: D

Ideal gas equation, for an adiabatic process is

PVγ=P{V^\gamma } = PVγ= constant ⇒\Rightarrow⇒ P1V1γ=P2V2γ{P_1}V_1^\gamma = {P_2}V_2^\gamma P1​V1γ​=P2​V2γ​

For monoatomic gas γ=53\gamma = {5 \over 3}γ=35​

∴\therefore∴ P1V15/3=P2(V18)5/3{P_1}V_1^{5/3} = {P_2}{\left( {{{{V_1}} \over 8}} \right)^{5/3}}P1​V15/3​=P2​(8V1​​)5/3

⇒\Rightarrow⇒ P2 = P1 × (2)5 = 32 P1.

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