Pressure of ideal gas at constant volume is proportional to _______.
1
average potential energy of the molecules
2
total energy of the gas.
3
average kinetic energy of the molecules
4
force between the molecules
Official Solution
Correct Option: (3)
Given:
An ideal gas is kept at constant volume.
Step 1: Understanding Pressure in Terms of Molecular Motion
According to the kinetic theory of gases, the pressure of an ideal gas is given by:
where is the average kinetic energy of the molecules.
Step 2: Identifying the Correct Answer
From the equation above, we see that pressure is directly proportional to the average kinetic energy of the molecules.
Answer: The correct option is C.
02
PYQ 2026
medium
physicsID: kcet-202
The graph of pressure P and volume V of 1 mole of an ideal gas at constant temperature is
1
Graph-I
2
Graph-II
3
Graph-III
4
Graph-IV
Official Solution
Correct Option: (4)
Step 1: Understanding the Question:
The question asks to identify the correct Pressure-Volume (P-V) graph for an ideal gas undergoing an isothermal process (constant temperature). Step 2: Key Formula or Approach:
For an ideal gas, the ideal gas law is .
In an isothermal process, temperature ( ) is constant, and for 1 mole, . So, .
This implies . This is the mathematical form of Boyle's Law. Step 3: Detailed Explanation:
A graph of versus where their product is constant ( ) will be a rectangular hyperbola.
Let's examine each graph:
- Graph-I: Shows pressure (P) remaining constant as volume (V) changes. This represents an isobaric process.
- Graph-II: Shows a linear relationship where . This is not isothermal.
- Graph-III: Shows a linear relationship where decreases linearly with . This is also not isothermal.
- Graph-IV: Shows a curve where decreases as increases, and the product remains constant. This is characteristic of a rectangular hyperbola, which correctly represents an isothermal process. Step 4: Final Answer:
Graph-IV correctly depicts the relationship between pressure and volume for an ideal gas at constant temperature.
