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A balloon contains $1.2m^{3}$ air at 15°C. Find its volume at 40°C. The thermal coefficient of volume expansion of air is $3.67\times〖10〗^{-3}  K^{-1}$. $(1.3m^{(3)}$

Difficulty: Easy

Solution:       Original volume = $V_{(0=)} 1.2m^{3}$
                      Initial temperature = $T_{0}$ = 15°C = 15 + 273 = 288 K
                       Final temperature = T = 40°C = 40 + 273 = 313 K
                        Change in temperature = $\triangle T$ = T - $T_{0}$ = 313 – 288 = 25 K
                        Coefficient of volume expansion of air $\beta$ = $3.67 \times 10^{-3} K^{-1}$ 
                        Volume = V = ?
                        V = $V_{0} (1+ \beta \triangle T)$
                        V = $1.2 (1 + 3.67 \times 10^{-3}\times25)$= $1.2(1+ 91.75 \times 10^{-3})$
                            = 1.2(1 + 0.09175) = $1.2\times 1.09175$
                        V = $1.3m^{3}$
                                                       

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