When an immersion glass thermometer is used to measure the...

When an immersion glass thermometer is used to measure the temperature of a liquid, the temperature reading will be affected by an error due to heat transfer between the liquid and the thermometer. Suppose you want to measure the temperature of $6.00 \mathrm{~mL}$ of water in a Pyrex glass vial thermally insulated from the environment. The empty vial has a mass of $5.00 \mathrm{~g}$. The thermometer you use is made of Pyrex glass as well and has a mass of $15.0 \mathrm{~g}$, of which $4.00 \mathrm{~g}$ is the mercury inside the thermometer. The thermometer is initially at room temperature $\left(20.0^{\circ} \mathrm{C}\right) .$ You place the thermometer in the water in the vial and, after a while, you read an equilibrium temperature of $29.0^{\circ} \mathrm{C} .$ What was the actual temperature of the water in the vial before the temperature was measured? The specific heat capacity of Pyrex glass around room temperature is $800 . J /(\mathrm{kg} \mathrm{K})$ and that of liquid mercury at room temperature is $140 . \mathrm{J} /(\mathrm{kg} \mathrm{K})$

Key Concepts

Calorimetry

Calorimetry involves the measurement and calculation of heat exchange between substances during physical or chemical changes. It relies on the principle of conservation of energy where the heat lost by one component is equal to the heat gained by another, allowing us to determine unknown temperatures, heat capacities, or enthalpy changes in a system.

Thermal Equilibrium

Thermal equilibrium is the state achieved when interacting objects reach the same temperature because there is no net heat transfer between them. This concept is fundamental in heat exchange problems, as it underpins the basis for calculating final temperatures when systems with different initial temperatures come into contact.

Specific Heat Capacity

Specific heat capacity is the amount of heat required to raise the temperature of a unit mass of a substance by one degree Celsius (or Kelvin). This property is essential in calorimetry calculations because it determines how much energy is absorbed or released by a substance as its temperature changes.

Transcript

00:01 So we can say the heat lost by the water would be equaling the mass of the water times the specific heat capacity of the water, multiplied by t, the equilibrium temperature, minus the initial temperature of the water.

00:16 We have the heat gained by the pyrex glass, plus the heat gained by the mercury.

00:30 And instead of, we can just say hg, that's better.

00:34 This would be equalling to the mass of the pyrex times the specific heat capacity of the pyrex multiplied by the equilibrium temperature minus the initial temperature of the pyrex plus the mass of the mercury, specific heat capacity of the mercury multiplied by the equilibrium temperature minus the initial temperature of the mercury.

01:00 And in this case we can say that the mass of the water times the specific heat capacity of the water times t minus the temperature, the initial temperature of the water plus the mass of the pyrex c sub p, t minus t sub p, plus mass of the mercury, specific heat capacity of the mercury, multiplied by the equilibrium temperature minus the initial temperature of the mercury.

01:38 This should be equalling zero.

01:40 And so we can then solve for the, temperature of the water and the initial temperature of the water would then be equaling to then the mass of the pyrex times the specific heat capacity of the pyrex plus the mass of the mercury multiplied by the specific heat capacity of the mercury multiplied by the the sum multiplied by the difference between the equilibrium temperature and the initial temperature of the mercury and the initial and this is simply because the temperature of the mercury and the pyrex are at the same initial temperature.

02:27 So we can say plus then the mass of the water, specific heat capacity of the water, times the equilibrium temperature.

02:40 This would be all divided by the mass of the water times the specific heat capacity of the water.

02:49 And so we can further simplify.

02:56 This would be then the essentially the exact same thing, except that you can split this fraction up into two and simply add on the equilibrium temperature.

03:15 So we have m -s -p, c -p plus the mass of the mercury, specific key capacity of the mercury.

03:23 The sum multiplied it by t minus t -sub -h -g...

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