A 50.0 g thermometer is used to measure the temperature of...

A $50.0 \mathrm{g}$ thermometer is used to measure the temperature of $200 \mathrm{ml}$ of water. The specific heat of the thermometer, which is mostly glass, is $750 \mathrm{J} / \mathrm{kg} \mathrm{K},$ and it reads $20.0^{\circ} \mathrm{C}$ while lying on the table. After being completely immersed in the water, the thermometer's reading stabilizes at $71.2^{\circ} \mathrm{C}$. What was the actual water temperature before it was measured?

Key Concepts

Heat Transfer in Calorimetry

Calorimetry involves measuring the amount of heat exchanged in a physical or chemical process. The method relies on understanding how different substances exchange heat and reach thermal equilibrium, allowing one to calculate unknown temperatures or heat capacities using the measured temperature changes.

Thermal Equilibrium

This concept refers to the state in which two or more objects in thermal contact no longer exchange energy, as they reach the same temperature. The final equilibrium temperature is determined by the masses and specific heat capacities of the substances involved.

Specific Heat Capacity

This is a property of a material that indicates the amount of heat required to change the temperature of one unit of mass by one degree Celsius or Kelvin. It is crucial in calculating the heat transfer between substances when their temperatures change.

Conservation of Energy

In thermodynamics, this principle states that in an isolated system the total energy remains constant. When two bodies at different temperatures come into contact, the heat lost by the hotter body is equal to the heat gained by the cooler body, ensuring the overall energy is conserved.

Transcript

00:01 Okay, so the water and thermometer will eventually reach a thermal equilibrium, which will have q1 is equal to q2.

00:07 Q1 is the heat that was generated by the water during this process, and q2 is the heat that was generated by the thermometer during this process.

00:15 So if a negative m1, c1, t1, t1, t1, it's equal to m2, c2, t2, t33.

00:19 So t3 thermal is the equilibrium temperature, and t1i is the initial temperature for the water, which is the temperature we are looking for to determine.

00:28 And t2i is the initial temperature of a thermometer.

00:30 So if we do some arrangement here, we have t1i is equal to m2c2x2 -t thermal minus m2c210t thermal divided by m1c1c1.

00:42 So we know the mass of the thermometer is given as 50 grams.

00:45 If we convert to kilograms, it's 0 .05 kilograms.

00:49 In the specific heat for the thermometer is given as 50 jou per kilogram times kelvin, and thermal equilibrium temperature is 71 .2 degrees celsius.

00:57 If we convert to kelvin, it's 34 .2 kelvin.

01:01 And the initial temperature for the thermal meter is 20 degrees celsius, which is 293 kelvin.

01:08 The mass of water is equal to density water, tens of volume of water.

01:12 And we know the density water is 1 ,000 kilogram per meter cube.

01:15 And the volume is given as 200 millimeter.

01:17 If we convert to a meter cube, it's 2 times 10 -2 -8 -4 meter cube.

01:20 So eventually we have the mass of water is equal to 0 .2 kilogram.

01:24 And the specific heat for the water is 4190 per kilogram times kelvin.

01:28 So now we can determine the initial temperature, or the water, which is t1i, is equal to m2c2, which is 0 .05 kilogram times 750, jew per kilogram times kelvin, and n times, let me see, t thermal, which is 344 .0 .2 kelvin minus 0 .05 kilogram times 750 jew per kilogram...

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