What is the effect on the pressure of a gas if its temperature is increased at constant volume ?

Options

A. The pressure of the gas increases.
B. The pressure of the gas decreases .
C. The pressure of the gas remains same .
D. The pressure of the gas becomes half.

Answer

To solve the question, "What is the effect on the pressure of a gas if its temperature is increased at constant volume?", we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Conditions**: The question states that the volume of the gas is constant. This means that we are looking at a scenario where the gas is not allowed to expand or contract.

**Hint**: Identify the key conditions in the problem, which are constant volume and changing temperature.

2. **Recall the Relevant Gas Law**: The relationship between pressure and temperature at constant volume is described by Gay-Lussac's Law. According to this law, the pressure of a gas is directly proportional to its absolute temperature when the volume is held constant.

**Hint**: Remember that Gay-Lussac's Law is crucial for understanding the relationship between pressure and temperature.

3. **Formulate the Relationship**: Mathematically, Gay-Lussac's Law can be expressed as:
\[ \frac{P_1}{T_1} = \frac{P_2}{T_2} \]
where \(P\) is the pressure, \(T\) is the absolute temperature (in Kelvin), and the subscripts 1 and 2 refer to the initial and final states of the gas, respectively.

**Hint**: Use the formula to relate initial and final states of pressure and temperature.

4. **Analyze the Effect of Increasing Temperature**: If the temperature \(T\) increases (while volume remains constant), then according to the equation, the pressure \(P\) must also increase to maintain the equality. This indicates a direct relationship.

**Hint**: Think about how increasing one variable (temperature) affects the other variable (pressure) in a direct relationship.

5. **Conclusion**: Therefore, if the temperature of the gas is increased while keeping the volume constant, the pressure of the gas will also increase.

**Hint**: Summarize your findings clearly to answer the question directly.

### Final Answer:
When the temperature of a gas is increased at constant volume, the pressure of the gas also increases.