For an ideal gas, under isobaric condition, a graph between log V vs log T :

Options

A. is linear with unit slope
B. represents Boyle’s Law
C. represents Charle’s Law
D. represents Gay-Lussac’s Law

Explanation

To solve the question regarding the graph between log V vs log T for an ideal gas under isobaric conditions, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Ideal Gas Law**:
The ideal gas law is given by the equation:
\[ PV = nRT \]
where \( P \) is the pressure, \( V \) is the volume, \( n \) is the number of moles, \( R \) is the universal gas constant, and \( T \) is the absolute temperature.

**Hint**: Remember that the ideal gas law relates pressure, volume, temperature, and the number of moles.

2. **Identify Isobaric Conditions**:
Under isobaric conditions, the pressure \( P \) remains constant. This means we can express the relationship between volume and temperature while keeping \( P \) constant.

**Hint**: Isobaric means pressure does not change; focus on how volume and temperature relate under this condition.

3. **Establish the Relationship**:
Since \( P \) is constant, we can rearrange the ideal gas law to show that volume \( V \) is directly proportional to temperature \( T \):
\[ V \propto T \]
This indicates that as temperature increases, volume also increases.

**Hint**: Think about direct proportionality—if one increases, the other must also increase.

4. **Convert Proportionality to an Equation**:
We can express this relationship as:
\[ V = kT \]
where \( k \) is a constant.

**Hint**: This equation shows a linear relationship between volume and temperature.

5. **Take the Logarithm of Both Sides**:
Taking the logarithm of both sides gives:
\[ \log V = \log(kT) = \log k + \log T \]
This can be rearranged to:
\[ \log V = \log T + \log k \]

**Hint**: Remember that the logarithm of a product is the sum of the logarithms.

6. **Identify the Linear Relationship**:
The equation \( \log V = \log T + \log k \) is in the form of a straight line \( y = mx + c \), where:
- \( y = \log V \)
- \( x = \log T \)
- \( m = 1 \) (slope)
- \( c = \log k \) (y-intercept)

**Hint**: Recognize that this represents a linear graph with a slope of 1.

7. **Conclusion**:
Since the graph of \( \log V \) versus \( \log T \) is linear with a unit slope, it represents Charles' Law, which states that at constant pressure, the volume of a gas is directly proportional to its absolute temperature.

**Hint**: Recall that Charles' Law specifically deals with volume and temperature at constant pressure.

### Final Answer:
The graph between log V vs log T for an ideal gas under isobaric conditions is linear with a unit slope and represents Charles' Law.