Volume-temperature graph at atmospheric pressure for a monoatomic gas `(V" in "m^3,T" in """^@C)` is

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Explanation

To determine the volume-temperature graph for a monoatomic gas at atmospheric pressure, we can use the ideal gas law and analyze the relationship between volume and temperature. 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
- \( V \) = volume
- \( n \) = number of moles
- \( R \) = universal gas constant
- \( T \) = temperature in Kelvin

### Step 2: Rearranging the Ideal Gas Law
We can rearrange the ideal gas law to express volume \( V \) in terms of temperature \( T \):
\[ V = \frac{nRT}{P} \]

### Step 3: Convert Temperature to Kelvin
Since the temperature \( T \) is given in degrees Celsius, we need to convert it to Kelvin:
\[ T(K) = T(°C) + 273 \]

### Step 4: Substitute Temperature into the Volume Equation
Substituting the expression for \( T \) into the volume equation gives:
\[ V = \frac{nR(T + 273)}{P} \]

### Step 5: Identify the Linear Relationship
This equation can be rewritten as:
\[ V = \frac{nR}{P} T + \frac{nR \cdot 273}{P} \]
This is in the form of a linear equation \( y = mx + c \), where:
- \( y \) is \( V \)
- \( x \) is \( T \)
- \( m \) (the slope) is \( \frac{nR}{P} \)
- \( c \) (the y-intercept) is \( \frac{nR \cdot 273}{P} \)

### Step 6: Analyze the Graph
From the linear equation, we can conclude:
- The slope \( m \) is positive, indicating that as temperature increases, volume also increases.
- The y-intercept \( c \) is also positive, which means that when \( T = 0 \) (in Celsius), the volume is still positive.

### Conclusion
The volume-temperature graph for a monoatomic gas at atmospheric pressure will be a straight line with a positive slope, starting from a positive y-intercept.