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Which of the following curve is correct ...

Which of the following curve is correct for a given amount of an ideal gas at constant pressure?

A

B

C

D

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The correct Answer is:
To determine the correct curve for a given amount of an ideal gas at constant pressure, we can analyze the relationship between volume (V) and temperature (T) using the ideal gas law. ### Step-by-Step Solution: 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 of gas - \( R \) = ideal gas constant - \( T \) = temperature in Kelvin 2. **Constant Pressure Condition**: Since we are considering a constant pressure scenario, we can rearrange the ideal gas law to focus on volume and temperature: \[ V = \frac{nRT}{P} \] Here, \( \frac{nR}{P} \) is a constant (let's call it \( k \)). Thus, we can write: \[ V = kT \] 3. **Relationship Between V and T**: From the equation \( V = kT \), we see that volume (V) is directly proportional to temperature (T) when pressure is constant. This means that if we plot V against T, we will get a straight line that passes through the origin (0,0). 4. **Graphical Representation**: If we multiply both sides of the equation \( V = kT \) by temperature (T), we get: \[ VT = kT^2 \] This indicates a parabolic relationship between \( VT \) and \( T \), which is a quadratic equation. However, since we are interested in the linear relationship between \( V \) and \( T \), we focus on the original equation. 5. **Analyzing the Options**: - The first option suggests a constant value for \( VT \), which is incorrect as \( VT \) varies with \( T^2 \). - The second option shows a graph of \( VT \) versus \( T^2 \), which should be a straight line starting from the origin. - The third option also shows a linear relationship starting from the origin. 6. **Conclusion**: The correct graph for a given amount of ideal gas at constant pressure is the one that represents a linear relationship between \( VT \) and \( T^2 \), starting from the origin. Thus, the answer is the third option.
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When a sample of ideal gas is changed from an initial state to a final state, various curves can be plotted for the process like P-V curve, V-T curve,P-T curve etc. For example, P-V curve for a fixed amount of an ideal gas at constant temperature is a rectangular hyperbola, V-T curve for a fixed amount of an ideal gas at constant volume is again a straight line. However, the shapes may vary if the constant parameters are also changed. Now, answer the following questions : Two Vander waals gases have same value 'b' but different 'a' value then which of the following statement is correct under simialr condition .