The Solar Balloon Challenge · AI Generator #GEN-D3D0BB2F

Physics · thermodynamics

Problem

A transparent spherical balloon of radius

R = 2.0\;\text{m}

is filled with air at atmospheric pressure

P_0 = 1.0 \times 10^5\;\text{Pa}

and initial temperature

T_0 = 290\;\text{K}

. The balloon material is massless and perfectly flexible, so the internal pressure always equals the external atmospheric pressure. When exposed to sunlight, the air inside absorbs solar energy at a rate of

\dot{Q} = 800\;\text{W}

. As the air heats up, the balloon expands while maintaining constant pressure. The air can be treated as an ideal diatomic gas with

C_V = \frac{5}{2}R_{gas}

and

C_P = \frac{7}{2}R_{gas}

, where

R_{gas} = 8.314\;\text{J/(mol·K)}

is the universal gas constant. The molar mass of air is

M = 0.029\;\text{kg/mol}

. (a) Find the initial number of moles of air in the balloon. (b) After heating for

t = 300\;\text{s}

, what is the final temperature of the air? (c) What is the final radius of the balloon?

Related theory

thermodynamics

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