Sample Problems on Kinetic Theory of Gases
Problem 1: A gas occupies 10 liters at a pressure of 30 mmHg. What will be the volume when the pressure is increased to 50 mmHg?
Solution:
Applying Boyle’s law,
P1V1 = P2V2
Now,
- P1 = 30 mmHg
- V1 = 10 liters
- P2 = 50mmHg
30 × 10 = 50 × V2
V2 = 6 liters
Problem 2: A gas occupies a volume of 300 cm3. Upon heating it to 200° Celsius, the volume increases to 1500 cm3. Find the initial temperature of the gas.
Solution:
According to Charles’s law,
V1T2 = V2T1
- V1 = 300 cm3
- T2 = 200° C
- V2 = 1500 cm3
300 × 200 = T1 × 1500
T1 = 40° C
Problem 3: A gas occupies 15.5 liters at a pressure of 55 mmHg. What will be the volume when the pressure is increased to 75mmHg?
Solution:
Applying Boyle’s law,
P1V1 = P2V2
Now,
- P1 = 55 mmHg
- V1 = 15.5 liters
- P2 = 75 mmHg
55 × 15.5 = 75 × V2
V2 = 11.36 liters
Problem 4: The root mean square speed of a gas molecule at 300K temperature and 2 bar pressure is 2 × 104 cm/sec. If the temperature is increased two times, find the new root mean square speed of the gas molecule.
Solution:
Formula for the root mean speed, vrms =
Therefore, v ∝ √T
v1/v2 = √T1/ √T2
- V1 = 2 × 104 cm/sec
- T1 = 300K
- T2 = 2 × 300 = 600K
(2 × 104)/v2 = √300/√600
v2 = 2√2 × 104 cm/sec
Kinetic Theory of Gases
Kinetic Theory of Gases is a theoretical model which helps us understand the behavior of gases and their constituent particles. This theory suggests that gas is made up of a larger number of tiny particles which collide with each other and their surroundings and exchange kinetic energy between them. The kinetic theory of gases has various applications throughout physics, chemistry, and engineering and it is essential to understand many phenomena like diffusion, effusion, and Brownian motion.
In this article, we will learn about the assumptions of kinetic theory, its limitations, and others in detail.