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Pullinger's apparatus to determine the coefficient of linear expansion

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Pullinger's Apparatus: Coefficient of Linear Expansion

Pullinger's Apparatus

Figure: Pullinger's Apparatus

Pullinger's apparatus is a laboratory instrument used to determine the coefficient of linear expansion of a metal rod.

Description

A long cylindrical metal steam jacket (or hollow tube) encloses the experimental metal rod AB. The thermometer T is inserted into the side of the jacket to measure the temperature of the system (steam/rod environment). A spherometer is placed at the top on a stable base plate to precisely measure the tiny change in the rod's length. A galvanometer (G) is connected to a battery through the key (K) to signal the accurate reading position when an electrical contact is established.

Working Principle

The initial length of the rod \((L_1)\) is measured at room temperature \((\theta_1)\). With the lowering of the central leg of the spherometer, the initial spherometer reading \((R_1)\) is recorded. Steam is then passed into the jacket through the inlet. As the steam heats the rod, the rod expands vertically upward (since base B is rigidly fixed).

Once the temperature stabilizes, the spherometer is again lowered until it touches the expanded rod, providing the final reading \((R_2)\).

$$\text{Increase in length, } \Delta L = L_2 - L_1 = R_2 - R_1$$

Hence, the coefficient of linear expansion \((\alpha)\) is given by:

$$\alpha = \frac{\Delta L}{L_1 \cdot \Delta \theta}$$ $$\therefore \alpha = \frac{R_2 - R_1}{L_1 \cdot (\theta_2 - \theta_1)}$$

In this way, the linear expansivity is determined. The superficial expansivity can also be determined by multiplying the above value by \(2\) (\(\beta = 2\alpha\)), and the cubical expansivity can be similarly determined by multiplying it by \(3\) (\(\gamma = 3\alpha\)).

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