According to the kinetic theory of gases, the average kinetic energy of gas molecules is d… — JAMB UTME

According to the kinetic theory of gases, the average kinetic energy of gas molecules is directly proportional to the absolute temperature. If a sample of nitrogen gas at an initial temperature of $27^\circ\text{C}$ is heated until the average kinetic energy of its molecules is tripled, what is the final temperature of the gas in $^\circ\text{C}$ ?

$627^\circ\text{C}$ Answer
B
$81^\circ\text{C}$
C
$900^\circ\text{C}$
D
$1173^\circ\text{C}$

Answer

The final temperature of the gas is

627^\circ\text{C}

According to the kinetic theory of gases, the average kinetic energy of gas particles is directly proportional to the absolute temperature in Kelvin (

E_k \propto T

). Converting the initial temperature

27^\circ\text{C}

to Kelvin yields

27 + 273 = 300\text{ K}

. Tripling the average kinetic energy means tripling the absolute temperature to

3 \times 300\text{ K} = 900\text{ K}

. Converting this back to degrees Celsius gives

900 - 273 = 627^\circ\text{C}

Step-by-Step Solution

Convert the initial temperature from Celsius to Kelvin.

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

Kinetic molecular theory states that average kinetic energy is directly proportional to absolute temperature (

E_k \propto T

in Kelvin).

Calculate the new absolute temperature after tripling the kinetic energy.

T_2 = 3 \times T_1 = 3 \times 300\text{ K} = 900\text{ K}

Tripling the average kinetic energy directly triples the absolute temperature in Kelvin.

Convert the final absolute temperature back to degrees Celsius.

t_2 = 900\text{ K} - 273 = 627^\circ\text{C}

The question explicitly requests the final temperature in degrees Celsius (

t = T - 273

Key Concept

Relationship between average kinetic energy and absolute temperature in the kinetic molecular theory

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