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KVPY2019PhysicsThermodynamics

A hot air balloon with a payload rises in the air. Assume that the balloon is spherical in shape with diameter of 11 . 7   m and the mass of the ballon and the payload (without the hot air inside) is 210   kg Temperature and pressure of outside air are 27 ° C and 1 atm = 10 5   N / m 2 , respectively. Molar mass of dry air is 30   g . The temperature of the hot air inside is close to [The gas

Options

  1. A27 ° C
  2. B52 ° C
  3. C105 ° C
  4. D171 ° C

Correct answer

C. 105 ° C

Step-by-step solution

Hot air balloon will rise in the atmosphere when upthrust of buoyant force is greater than weight of balloon and its payload. Upthrust = Weight of atmospheric air displaced by balloon So, upthrust ≥ weight of balloon and its payload ⇒ (Volume of air displaced × density of atmospheric air × Acceleration due to gravity) ≥ (Volume of air of inside balloon x density of air inside balloon × acceleration due to gravity) + (Weight of payload of balloon) ⇒ V · ρ o · g &

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