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9 December, 09:58

Before heating a hot air balloon, the air temperature is 20C, and the density of air is 1 kg/m3. To launch the balloon, the burner is lit, and the air temperature inside the balloon is raised to 30C. What is the air density in the balloon now?

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Answers (2)
  1. 9 December, 12:56
    0
    density and temperature have an inverse relationship between them. initial density = 1 kg/m3 initial temperature = 20C = 293k final temperature = 30C = 303k final density = ?

    ρT = K

    ρ1T1 = ρ2T2

    ρ2 = ρ1T1/T2

    = 1 X 293 / 303

    = air density in the balloon now = 0.967kg/m3
  2. 9 December, 13:53
    0
    p_2 = 0.967 kg/m^3

    Explanation:

    Given:

    - Initial Temperature T_1 = 20 C

    - Final Temperature T_2 = 30 C

    - Initial Density of air p_1 = 1 kg/m^3

    Find:

    The Density of air after heating.

    Solution:

    - The air can be idealized and expressed using Ideal Gas Law as follows:

    P = p*R*T

    Where,

    P = Absolute pressure

    R = Gas constant for air

    T = Absolute Temperature

    - We know that the pressure P of the air remains constant at 1 atm.

    P_1 / R = P_2/R

    p_1*T_1 = p_2*T_2

    p_2 = p_1 * (T_1 / T_2)

    Plug in the values:

    p_2 = 1 * (20+273 / 30+273)

    p_2 = 0.967 kg/m^3
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