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?

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

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