Quantitative Reasoning- Passage Based- Temperature of substances on different scales!

2014_QNR 11. The temperature of a substance indicates how energetic that substance’s particles are. The particles in a hot object are highly energetic, moving rapidly and colliding with each other frequently. The particles in a colder object move more slowly, collide less often and have very low energy.
Over the centuries, scientists have created temperature scales to describe how hot or how cold substances are.
All temperature scales use the term degree as a basic unit. However, the size of these degrees is different on each of the temperature scales because the scientists who developed them defined the freezing point and boiling points of water in different ways.
The most widely used temperature scale is the Celsius scale which defines the freezing point of water as 0 degrees Celsius (written as 0ºC) and its boiling point as 100ºC.
The Newton scale, developed by Isaac Newton in 1700, also defines the freezing point of water as its zero point, but defines the boiling point of water as 33 Newton degrees (or 33ºN). (A Newton temperature N is converted to its equivalent Celsius temperature C by using the equaion N X 100/33 =C).
The Fahrenheit scale, which is still used in many parts of the world, defines Water’s freezing point as 32ºF and its boiling point as 212ºF. (A Fahrenheit temperature F is converted into its equivalent Celsius temperature C by using the equation:(F – 32) X 5 / 9 = C).
Scientists describe the point at which the particles of a substance have no energy at all, as absolute zero.
The Kelvin scale uses absolute zero as its starting temperature point (0 K). On this scale, water freezes at 273.15 K and boils at 373.15 K. (A Kelvin temperature K is converted into its equivalent Celsius temperature C by using the equation: K – 273.13 = C)

(i)  A Celsius degree is nearly
(1) one hundredth the size of a Newton degree.
(2) the same size as a Newton degree.
(3) 33 times the size of a Newton degree.
(4) one third the size of a Newton degree.

(ii) What temperature is absolute zero on the Newton temperature scale ?
(1) 273.15ºN

(2) –827.7ºN
(3) –273.15ºN

(4) –90.1ºN

(iii)  The hottest temperature on Earth was 160ºF,
recorded in Libya on September 13, 1922. This
temperature is equivalent to
(1) 113 K

(2) 71ºC
(3) 71 K

(4) 89ºC

(iv) Which one of the following graphs may be used to convert correctly between Celsius and Kelvin scales?

2014_QNR 11

Ans: (i) Given : N*100/33 =C

As per the relation given in the passage one Celsius should be more than 3 times the size of a Newton degree. None of the options fit in here. What’s the problem then?

The problem is the wrong relationship given in the passage. As per the passage boiling water temperature is 33 deg N which should be same as 100 deg C. The correction expression should be N*33/100 = C.

If you google the relationship between N and C, you could verify the above expression.In that case the answer option 4 will fit in.

(ii) Using the expression K – 273.13 = C, at absolute temperature K=0, C= -273.13

Now, using N*33/100= C  => N = 100*C/33 = 100 (-273.13)/33 ~ (1/3)* (-273.13) ~-91.04.

Since 1/3 is the approximation of 100/3, the actual absolute value will be bit less than 91.04. Option 4

(iii) Let us convert 160ºF into K and C.

(F – 32) X 5 / 9 = C

=> C= (160-32)*5/9= 128*5/9= 640/9= 71.1 deg

Also, K – 273.13 = C

=>K = 71.1 + 273 = 344 deg. Option 2.

(iv) Celsius-Kelvin relationship is given by:

K = °C + 273.15  —(A)

(1) Rejecting out this option as the relationship is “directly proportional“; increase in C should bring about increase in Kelvin.

(2) Rejecting out this option as relationship is linear. Graph is not a straight line.

(3) Rejecting out this option as when K is zero (point lying on C axis), C is supposed to be negative (-273.15). C is shown positive in the graph.

(4) Correct option.

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