(a) P₂ / P₁ = 2 / 1
(b) P₂ / P₁ = 17.93 / 13
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
A. The ratio of final pressure to the initial pressure (P₂ / P₁) when the temperature of the gas rises from 39 to 78 K is 2 / 1
B. The ratio of final pressure to the initial pressure (P₂ / P₁) when the temperature of the gas rises from 39 to 53.8 °C is 817 / 780
A. Determination of the The ratio of final pressure to the initial pressure (P₂ / P₁) when the temperature of the gas rises from 39 to 78 K
Initial temperature (T₁) = 39 K
Final temperature (T₂) = 78 K
Volume = constant
P₁ / T₁ = P₂ / T₂
P₂ / P₁ = T₂ / T₁
P₂ / P₁ = 78 / 39
B. Determination of the The ratio of final pressure to the initial pressure (P₂ / P₁) when the temperature of the gas rises from 39 to 53.8 °C
Initial temperature (T₁) = 39 °C = 39 + 273 = 312 K
Final temperature (T₂) = 53.8 °C = 53.8 + 273 = 326.8 K
Volume = constant
P₁ / T₁ = P₂ / T₂
P₂ / P₁ = T₂ / T₁
P₂ / P₁ = 326.8 / 312
P₂ / P₁ = 3268 / 3120
P₂ / P₁ = 3268 / 3120
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