Answer:
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
