Two metal strips that constitute a thermostat must necessarily differ in their

The correct option is Coefficient of linear expansion.

Understanding Bimetallic Strips in Thermostats:
A thermostat typically uses a bimetallic strip to sense and respond to temperature changes. This strip is made by bonding together two different metal strips along their entire length.

Mechanism of Action:
When the temperature changes, materials expand or contract. The change in length of a metal strip due to thermal expansion is given by the formula:
$\Delta L=L_0\alpha \Delta T$
where:
- $\Delta L$ is the change in length,
- $L_0$ is the initial length,
- $\alpha$ is the coefficient of linear expansion, and
- $\Delta T$ is the change in temperature.

For the bimetallic strip to work as a switch, it must bend when heated or cooled. This bending occurs because the two bonded metals expand by different amounts when subjected to the same temperature change. The property that determines this difference in expansion rate is the coefficient of linear expansion ($\alpha$).

If the two metals had the same coefficient of linear expansion, they would expand at the exact same rate. Consequently, the strip would only increase in length without bending, making it impossible to open or close the electrical contacts in the thermostat.