Why Can't a Full-Size Thermometer Measure Thimbleful Hot Water Accurately?

[spaghetti3451]

Homework Statement

Explain why it would not make sense to use a full-size glass thermometer to measure the temperature of a thimbleful of hot water.

Homework Equations

Concept of thermal equilibrium

The Attempt at a Solution

When a thermometer is in contact into a thermal system, thermal energy flows from the system to the thermometer or vice-versa until thermal equilibrium is established between the thermometer and the system. In this process, the system gains or loses thermal energy and so the temperature of the system will have changed. Therefore, a thermometer can only accurately measure the temperature of a heat reservoir.

In this case, the full-size glass thermometer absorbs a significant amount of thermal energy from the thimbleful of hot water, so the temperature measured is highly inaccurate.

Can you please check my answer?

 

[rude man]

You have put it very well. You could also have mentioned relative heat capacities of the water vs. the thermometer.

 

[spaghetti3451]

Well, the thermal energy lost by the water equals the thermal energy gained by the thermometer. So, mcΔθ for the water equals mcΔθ for the thermometer. The mass and specific heat capacity of the water are smaller than those for the thermometer. So, the temperature change of the water is much larger compared to the temperature of the water. This implies that the temperature of the water will not be measured accurately.

Is that right? I'm not sure about the magnitude of the specific heat capacity of a mercury-in-tube thermometer, so I am not sure if my answer is fully correct.

 

[rude man]

Excellent! While you bring up a good point - the specific heat of water is among the highest of any known substances - higher than glass or Hg - the low m of the water would more than make up for its high c. So your equation is most appropriate.