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MHT CET202525 Apr 2025Evening ShiftPhysicsThermodynamicsActual

A balloon is filled at 27^ C and 1 atmospheric pressure by volume 500 ~m ^3 helium gas. At -3^0 C and 0.5 atmospheric pressure, the volume of helium gas will be

Options

  1. A500 ~m ^3
  2. B700 ~m ^3
  3. C900 ~m ^3
  4. D1000 ~m ^3

Correct answer

C. 900 ~m ^3

Step-by-step solution

The volume is determined using the combined gas law, which for a fixed amount of gas gives P₁ V₁ T₁ = P₂ V₂ T₂ . Convert temperatures to the absolute scale: T₁ = 27^ C + 273 = 300 K and T₂ = -3^ C + 273 = 270 K . Substitute the known values P₁ = 1 atm , V₁ = 500 m ^3 , and P₂ = 0.5 atm , then solve for V₂ : V₂ = P₁ V₁ T₂ P₂ T₁ = 1 500 270 0.5 300 = 135000 150 = 900 m ^3 . The helium occupies 900 m³ under the new conditions.

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