Final answer:
The temperature for a length of 4.0 cm in a liquid-in-glass thermometer is 20°C. The greatest increase in sensitivity for a thermometer is achieved by both increasing the volume of liquid and reducing the bore diameter.
Step-by-step explanation:
To calculate the temperature for a length of 4.0 cm, we use the given lengths at known temperatures to determine the scale of the thermometer. Given that 2.0 cm corresponds to 0°C (the temperature of melting ice) and 12.0 cm corresponds to 100°C (the temperature of steam), we can set up a linear relationship where every 1.0 cm increment represents 10°C ([12.0 cm - 2.0 cm] / [100° - 0°C] = 1.0 cm/10°C). Thus, for a 4.0 cm length, the temperature can be calculated as follows: (4.0 cm - 2.0 cm) × 10°C = 20°C.
The sensitivity of a liquid-in-glass thermometer can be affected by both the volume of the liquid and the diameter of the bore. A smaller bore diameter or larger volume of liquid will usually produce the greatest increase in sensitivity. This is because a smaller bore will cause a larger change in the length of the liquid column per degree of temperature change, and a larger volume of liquid will create more liquid to expand and contract with temperature changes. Therefore, the answer is c. Both volume of liquid and bore diameter.