A balloon contains 1.2 m³ air at 15°C. Find its volume at 40°C. The thermal coefficient of volume expansion of air is 3.67ｘ10⁻³K⁻¹. Ans. (1.3 m³)


Given:

Initial Volume of the air  = Vₒ = 1.2 m³
Initial Temperature = T₁ = 15°C = (15 + 273) K = 288 K
Final Temperature = T₂ = 40°C = (40 + 273) K = 313 K
Thermal Coefficient of Linear expansion of Aluminum = 𝜷 = 3.67 ｘ10⁻³ K⁻¹

To Find:

Final Volume of the air  = V  = ?

Solution:  


The formula for an increase in Volume is 

V - Vₒ  = 𝜷 Vₒ ( T₂  - T₁)

Or

V   = Vₒ + 𝜷 Vₒ ( T₂  - T₁)  

V   = Vₒ ( 1 + 𝜷 ( T₂  - T₁) )

by putting values 

V   = 1.2 m³ ( 1 + 3.67 ｘ10⁻³ K⁻¹ ( 313 K - 288 K) )

V   = 1.2 m³ ( 1 + 3.67 ｘ10⁻³ K⁻¹ ( 25 K) )

V   = 1.2 m³ ( 1 + 91.75 ｘ10⁻³)

V   = 1.2 m³ ( 1 + 0.09175)

V   = 1.2 m³ ( 1.09175)

V   = 1.310 m³

or

V   = 1.3 m³

Thus the final volume of air after heating is 1.3 m³

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