Question

A hot-air balloon has a pressure of 0.715 atm while the temperature outside is 200C. What will the pressure be if the temperature drops to 5C while the volume remains constant?

1.12 kPa

11.2 atm

1203 atm

1.12 atm

Answer 1

• If the temperature drops to 5⁰C and the volume remains constant, the value of pressure will be 0.668 atm.It can be found using Ideal gas equation.

What is Ideal gas equation ?

The ideal gas law (PV = nRT) relates the macroscopic properties of ideal gases. An ideal gas is a gas in which the particles (a) do not attract or repel one another and (b) take up no space (have no volume).

From the question given above, the following data were obtained :

• Initial pressure (P₁) = 0.715 atm
• Initial temperature (T₁) = 200 °C
• Final temperature (T₂) = 195 °C
• Volume = constant

• Final pressure (P₂) = ?

Now, Let's convert celsius temperature to Kelvin temperature ;

T(K) = T(°C) + 273

• Initial temperature (T₁) = 200 °C = 200 °C + 273  = 473 K

• Final temperature (T₂) = 195 °C = 195  °C + 273  = 462 K

Now, we shall can determine the final pressure (P₂)  ;

• Initial pressure (P₁) = 0.715 atm
• Initial temperature (T₁) = 473 K
• Final temperature (T₂) = 462 K
• Final pressure (P₂) = ?

P₁ / T₁ = P₂ / T₂

0.715 / 473 = P₂ /  462

473 × P₂ = 0.715 × 462

P₂ = 0.69 atm

Thus, the final pressure of the hot air balloon is 0.69 atm

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