Calculate the final absolute pressure of the oxygen gas inside the industrial storage vess… — JAMB UTME

Calculate the final absolute pressure of the oxygen gas inside the industrial storage vessel by completing the blank below.

Cevap:An industrial storage vessel containing oxygen gas at a fixed volume exerts a pressure of

180\text{ kPa}

at a temperature of

27^\circ\text{C}

. If the temperature of the gas rises to

127^\circ\text{C}

, the new pressure exerted by the gas will be 【240】 kPa.

The final pressure exerted by the oxygen gas is

240\text{ kPa}

According to Gay-Lussac's Pressure Law, for a fixed mass of gas at constant volume,

\frac{P_1}{T_1} = \frac{P_2}{T_2}

where temperature must be in Kelvin. Converting the temperatures:

T_1 = 27 + 273 = 300\text{ K}

and

T_2 = 127 + 273 = 400\text{ K}

. Rearranging for

P_2

gives

P_2 = 180 \times \frac{400}{300} = 240\text{ kPa}

Convert temperatures from Celsius to the Kelvin absolute scale

T_1 = 27^\circ\text{C} + 273 = 300\text{ K}

and

T_2 = 127^\circ\text{C} + 273 = 400\text{ K}

All gas law calculations require temperatures to be expressed in absolute units (Kelvin).

Apply the Pressure Law (Gay-Lussac's Law) mathematical formula

\frac{P_1}{T_1} = \frac{P_2}{T_2} \implies P_2 = P_1 \times \frac{T_2}{T_1}

At constant volume, the pressure of a given mass of gas is directly proportional to its absolute temperature.

Substitute the given numerical values into the formula and solve for

P_2

P_2 = 180\text{ kPa} \times \frac{400\text{ K}}{300\text{ K}} = 180 \times \frac{4}{3} = 240\text{ kPa}

Calculates the resulting pressure in kilopascals.

Pressure Law (Gay-Lussac's Law of Temperature-Pressure)

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