(I) At the boiling point of sulfur (444.6^∘ C) the pressure in a constant-volume gas thermometer

(I) At the boiling point of sulfur (444.6^∘ C) the pressure...

Key Concepts

Constant-Volume Gas Thermometry

This concept involves the use of a gas thermometer where the volume of the gas is kept constant. According to the ideal gas law, under constant volume, the pressure of the gas is directly proportional to its absolute temperature. This relationship allows the determination of temperature changes by simply measuring the changes in pressure, making it a reliable method for high-precision temperature measurements.

Ideal Gas Law

The ideal gas law, expressed as PV = nRT, is a fundamental equation in thermodynamics that relates the pressure, volume, temperature, and amount of an ideal gas. In scenarios where the volume is held constant, this law simplifies to show that pressure is directly proportional to absolute temperature (P ? T). This proportionality is key when using constant-volume gas thermometers.

Temperature Scales

In thermometry, it is crucial to work with the Kelvin scale because it is an absolute temperature scale starting from absolute zero, where all thermal motion ceases. Converting Celsius measurements to Kelvin is essential for calculations involving the ideal gas law, ensuring that the direct proportionality between pressure and temperature is correctly applied.

Transcript

00:02 So, at the boiling point of sulfur, 446 degrees celsius, 44 .6 degrees celsius, the pressure in a constant gas volume thermometer is 187 tall.

00:13 Estimate the pressure at the triple point water and the temperature when the pressure in the thermometer is 118 tall.

00:19 So we're going to briefly derive the gas thermometer equation because it seems to come out of nowhere in the book and it would be beneficial to derive it.

00:30 Understand it and then quickly do the question because it doesn't require that much once you understand where it comes from.

00:36 So starting from the two versions of the ideal gas law, so p1 v1 is equal to nr n1 r one n1 r um n r um n r t one so pressure volume is equal to number of moles times a gas constant times t1 and that's equation one.

00:59 Equation 2 is p1 v1 sorry p2 even v2 is equal to n to r t2 whoops one second so pvrt2 and that's equation 2 now we divide equation 1 by equation 2 to give p1 over p2 dot v1 over v2 is equal to n1 over n2 and times by dotted with t1 over t2.

01:46 Now, in a constant volume gas thermometer, we have a closed volume.

01:55 So volume 1 is equal to volume 2 in any fixed state.

01:58 And similarly, the number of moles is equal on both sides.

02:02 Hence, we have p1, p2 is equal to t1t2.

02:07 Now, what we can say is we can calibrate all our formometers, the triple point of water, and the triple point of water is given by 273 .16 celsius.

02:19 So we can say that t1 over the triple point of water, which is 273 .1.

02:29 Is equal to the pressure p1 over the pressure at the triple point of water ptp.

02:40 Now we can just, because we don't have t1 and t2, we just redenote these, relabel them as tmp, multiply through by 273 .16, and we get the t is equal to 273 .16 times by the pressure over the pressure at the triple point.

03:00 And that is the equation for the constant volume gas thermometer.

03:07 So we're given in the question, we're going to start a new whiteboard for this.

03:14 So we're given in the question that the temperature is given by 4 -4 .6.

03:23 So we're going to add on, we're test -make -the -pressure.

03:27 So we're going to make pressure...

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