<h2>
Answer:</h2>
(a) P₂ / P₁ = 2 / 1
(b) P₂ / P₁ = 17.93 / 13
<h2>
Explanation:</h2>
At constant volume, the pressure (P) of an ideal gas is directly proportional to its temperature (T) as stated by Joseph Gay-Lussac. i.e
P ∝ T
=> P = KT
=> P / T = K
=> (P₁ / T₁) = (P₂ / T₂) = K
=> (P₁ / P₂) = (T₁ / T₂) = K
=> (P₂ / P₁) = (T₂ / T₁) = K -----------------------(i)
Where;
P₁ and P₂ are the initial and final pressures of the gas.
T₁ and T₂ are the initial and final temperatures of the gas.
(a) if temperature rises from 39 to 78 K;
This implies that;
T₁ = 39 K
T₂ = 78 K
Substitute these values into equation (i) as follows;
=> (P₂ / P₁) = (78 / 39)
=> (P₂ / P₁) = (26 / 13)
=> (P₂ / P₁) = (2 / 1)
Therefore, the ratio P₂ / P₁ = 2 / 1
(b) if temperature rises from 39.0 to 53.8 K;
This implies that;
T₁ = 39.0 K
T₂ = 53.8 K
Substitute these values into equation (i) as follows;
=> (P₂ / P₁) = (53.8 / 39)
=> (P₂ / P₁) = (17.93 / 13)
Therefore, the ratio P₂ / P₁ = 17.93 / 13
