Question

Which of the following graph correctly represent the variation $\delta =\frac{dV}{VdT}$ for an ideal gas at constant pressure?

• A.
• B.
• C.
• D.

Answer 1

The Correct Option is D

To solve this problem, we need to understand the relationship between the given parameters for an ideal gas at constant pressure.

The equation provided is:

\[ \delta = \frac{dV}{VdT} \]

This expression represents the coefficient of volume expansion for an ideal gas at constant pressure. It describes how the volume of the gas changes with temperature when pressure is held constant.

For an ideal gas under constant pressure, the relationship between volume and temperature is governed by Charles's Law, which states:

\[ V \propto T \]

This implies that if the temperature increases, the volume of the gas will also increase linearly as long as the pressure is constant. Therefore, the graph of \(\frac{dV}{dT}\) should be a horizontal line since the rate of change of volume with temperature remains constant.

Given the options, the correct graph should be a horizontal line indicating the linear relationship at constant pressure. Upon examining the provided graphs, the graph that matches this behavior is:

This graph represents a constant coefficient of volume expansion \(\delta\), indicating that the volume change per unit temperature change remains the same under constant pressure.

Therefore, the correct answer is the graph with data-src-id="63e4af92bd1de63440142ca8", as it properly represents the relationship of volume with temperature for an ideal gas at constant pressure.