An ungraduated mercury thermometer attached to a millimeter scale reads 22.8 mm in ice and 242mm in steam at standard pressure. What will the millimeter read when the temperature is. 20oC?

assuming 100 degree steam

slope = (242 -22.8) /(100 -0)
= 2.19 mm/degree

so 22.8 + 2.19(20) = 66.6 mm

Well, well, well. Looks like we've got a thermometer playing it cool in ice and getting all steamed up in steam! But fear not, my friend, for I am here to clown around and help you out.

Now, let's tackle this temperature puzzle. Since we know that 22.8 mm is the reading in ice and 242 mm is the reading in steam, we need to find the corresponding reading for 20 degrees Celsius.

But before we dive in, let me ask you this: Did you know that thermometers have a tendency to exaggerate their feelings? They're just like some people I know! Always making a big fuss about a little change in temperature.

Alright, back to business! We'll need to interpolate to find the millimeter reading at 20 degrees Celsius. Interpolation is like finding the middle ground between two extreme measurements. So let's crank up the funny-o-meter and get calculating!

First, we need to find the difference between the two extremes:
Δmm = 242 mm - 22.8 mm = 219.2 mm

Then, we need to find the difference in temperature between the two extremes:
ΔT = (100 °C - 0 °C) = 100 °C

Now, we can calculate how many millimeters are associated with 1 degree Celsius:
(mm/°C) = Δmm/ΔT = 219.2 mm / 100 °C = 2.192 mm/°C

Finally, we can find the millimeter reading for 20 °C:
mm = (20 °C) x (2.192 mm/°C) + 22.8 mm
mm = 43.84 mm + 22.8 mm
mm = 66.64 mm

So, grab your popcorn and get ready for the grand finale! When the temperature is 20 °C, the millimeter reading on the ungraded mercury thermometer will be approximately 66.64 mm.

Remember folks, temperature conversions can be chilly, but with a little warmth from my humor, we'll get through it together!

To find out what the millimeter reading will be when the temperature is 20°C, we first need to determine the calibration points for the given thermometer.

The thermometer reads 22.8 mm in ice and 242 mm in steam at standard pressure. These points will be used to establish the linear relationship between temperature and millimeter reading.

Let's calculate the calibration equation:

Temperature in Celsius (T) Millimeter reading (M)
-----------------------------------------------------------
0°C 22.8 mm
100°C 242 mm

Using the two calibration points, we can find the slope (m) and y-intercept (b) of the equation of the line in the form y = mx + b:

Slope (m) = (M2 - M1) / (T2 - T1)
= (242 mm - 22.8 mm) / (100°C - 0°C)
= 219.2 mm / 100°C
= 2.192 mm/°C

Now that we have the slope, we can calculate the y-intercept (b) using one of the calibration points:

b = M1 - (m x T1)
= 22.8 mm - (2.192 mm/°C x 0°C)
= 22.8 mm

Therefore, the equation of the line relating temperature (T) to millimeter reading (M) is:

M = 2.192T + 22.8

Now we can substitute the desired temperature (20°C) into the equation to find the corresponding millimeter reading (M):

M = 2.192 x 20 + 22.8
= 43.84 + 22.8
= 66.64 mm

Therefore, the millimeter reading on the thermometer will be approximately 66.64 mm when the temperature is 20°C.

To determine the millimeter reading on the ungraduated mercury thermometer, we first need to establish a linear relationship between temperature and millimeter readings. This can be done by obtaining data points at reference temperatures and their corresponding millimeter readings.

In this case, we have two reference temperatures: the temperature of ice and the temperature of steam. The millimeter readings for these two temperatures are given as 22.8 mm and 242 mm, respectively.

To find the linear relationship, we start by calculating the temperature difference between the two reference points:

Temperature difference = Temperature of steam - Temperature of ice
= 100 °C (boiling point of water) - 0 °C (freezing point of water)
= 100 °C

Next, we calculate the millimeter difference between the two reference points:

Millimeter difference = Millimeter reading of steam - Millimeter reading of ice
= 242 mm - 22.8 mm
= 219.2 mm

Now we can calculate the linear relationship between temperature and millimeter readings:

Temperature change per mm = Temperature difference / Millimeter difference
= 100 °C / 219.2 mm

To find the millimeter reading at 20 °C, we calculate the temperature difference from the temperature of ice:

Temperature difference from ice = 20 °C - 0 °C
= 20 °C

Finally, we can calculate the millimeter reading:

Millimeter reading = Temperature difference from ice / (Temperature change per mm)
= 20 °C / (100 °C / 219.2 mm)

Simplifying the equation:

Millimeter reading = 20 °C * (219.2 mm / 100 °C)
= 43.84 mm

Therefore, when the temperature is 20 °C, the millimeter reading on the ungraduated mercury thermometer will be approximately 43.84 mm.