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?

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

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