A gas is contained in a thick-walled

balloon. When the pressure changes

from 18.7 psi to 20.2 psi, the volume

changes from 0.475 L to 1.054 L and

the temperature changes from

K to 465 K.

T₁ = 194 K

Solution:

Data Given:

Initial Temperature = T₁ = ?

Final Temperature = T₂ = 465 K

Initial Pressure = P₁ = 18.7 psi

Final Pressure = P₂ = 20.2 psi

Initial Volume = V₁ = 0.475 L

Final Volume = V₂ = 1.054 L

Formula Used:

Let's assume that the hydrogen gas in balloon is acting as an Ideal gas, the according to Ideal Gas Equation,

P V = n R T

where; R = Universal Gas Constant = 0.082057 atm. L. mol⁻¹. K⁻¹,

Taking number of moles and R constant we can have following formula for initial and final states,

P₁ V₁ / T₁ = P₂ V₂ / T₂

Solving for T₁,

T₁ = P₁ V₁ T₂ / P₂ V₂

Putting values,

T₁ = (18.7 psi * 0.475 L * 465 K) / (20.2 psi * 1.054 L)

T₁ = 194 K