At constant volume, temperature is increased. Then

Options

A. collision on walls will be less
B. number of collisions per unit time will increase
C. collisions will be in straight lines
D. collisions will not change

Answer

To solve the question "At constant volume, temperature is increased. Then," we can analyze the situation using the ideal gas law and the behavior of gases. Here’s a step-by-step solution:

### Step 1: Understand the Ideal Gas Law
The ideal gas law is given by the equation:
\[ PV = nRT \]
where:
- \( P \) = pressure of the gas
- \( V \) = volume of the gas
- \( n \) = number of moles of the gas
- \( R \) = ideal gas constant
- \( T \) = temperature of the gas (in Kelvin)

### Step 2: Identify the Given Conditions
In this problem, we are told that the volume \( V \) is constant and that the temperature \( T \) is increased.

### Step 3: Analyze the Effect of Increasing Temperature
Since the volume \( V \) and the number of moles \( n \) are constant, we can rearrange the ideal gas law to focus on pressure:
\[ P = \frac{nRT}{V} \]
From this equation, we can see that if \( V \) is constant and \( n \) is constant, then pressure \( P \) is directly proportional to temperature \( T \):
\[ P \propto T \]

### Step 4: Conclusion on Pressure
As the temperature \( T \) increases, the pressure \( P \) must also increase because they are directly proportional.

### Step 5: Relate Pressure to Molecular Collisions
An increase in pressure at constant volume implies that the gas molecules are colliding with the walls of the container more frequently. This is because higher temperature means that the molecules have more kinetic energy, leading to more collisions per unit time.

### Final Conclusion
Thus, at constant volume, when the temperature is increased, the number of collisions per unit time will increase.

### Answer
The correct conclusion is that **the number of collisions per unit time will increase**.

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