KVPY 2019 SA Exam Previous Papers

Question : 69 of 80

Marks: +1, -0

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 balloon 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. Thetemperature of the hot air inside is close to, [The gas constant R = 8.31 J/K/mol]

27°C
52°C
105°C
171°C

Validate

Solution:

210 g + ρ \inVg = ρ 0Vg

ρ \in

= density of air inside the balloon

ρ o

= density of air outside the balloon

ρ \in-ρo=210/V=210/{4/3πr^3}

{PM}/{RT_0}-{PM}/{RT_\in}={210× 3}/{4πr^3}

{PM}/R(1/T_0-1/T_\in)={210× 3}/{4πr^3}

1/T_0-1/T_\in={630 ×8}/{4π(11.7)^3}×{8.31}/{10^5×30×10^{-3}}≈ 0.0007

_\in ≈384 = 111°C

closest answer the option (C)

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