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Chapter 1: Q.1.1. (page 5)

The Fahrenheit temperature scale is defined so that ice melts at 320 F and water boils at 2120 F.

(a) Derive the formula for converting from Fahrenheit to Celsius and back

(b) What is absolute zero on the Fahrenheit scale?

Short Answer

Expert verified

(a)95掳C+32=掳F

(b) -459.67掳F

Step by step solution

01

Part (a) Step 1 : Fahrenheit scales values of freezing point and boiling point.

Fahrenheit freezing point of water = 32掳F

Fahrenheit boiling point of water = 212掳F

212 - 32 = 180掳F between the freezing point and boiling point of water.

02

Part (a) Step 2 :  Celsius scales values of freezing and boiling point.

Celsius freezing point of water = 0掳C

Celsius boiling point of water = 100掳C

100 - 0 = 100掳C between the freezing point and boiling point of water.

03

Part (a) Step 3 : Ratio for Celsius to Fahrenheit scale values. 

The ratio for Celsius to Fahrenheit of 100180=59and the ratio of Fahrenheit to Celsius of 180100=95

then 32掳F= 0掳C

Hence the formula for degree Celsius to Fahrenheit is localid="1649151785065" 95掳C+32=掳F

04

Part (b) Step 1: Absolute zero in celsius

Absolute zero = 0K

K - 273.15 = 掳C

掳C = 0 - 273.15 = -273.15掳C

05

Part (b) Step 2: Absolute zero in Fahrenheit

we know that 掳F=95掳C+32

掳F=95(-273.15)+32

掳F=-459.67掳F

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Most popular questions from this chapter

Problem 1.41. To measure the heat capacity of an object, all you usually have to do is put it in thermal contact with another object whose heat capacity you know. As an example, suppose that a chunk of metal is immersed in boiling water (100掳C), then is quickly transferred into a Styrofoam cup containing 250 g of water at 20掳C. After a minute or so, the temperature of the contents of the cup is 24掳C. Assume that during this time no significant energy is transferred between the contents of the cup and the surroundings. The heat capacity of the cup itself is negligible.

  1. How much heat is lost by the water?
  2. How much heat is gained by the metal?
  3. What is the heat capacity of this chunk of metal?
  4. If the mass of the chunk of metal is 100 g, what is its specific heat capacity?

Given an example to illustrate why you cannot accurately judge the temperature of an object by how hot or cold it feels to the touch?

An ideal diatomic gas, in a cylinder with a movable piston, undergoes the rectangular cyclic process shown in Figure 1.10(b). Assume that the temperature is always such that rotational degrees of freedom are active, but vibrational modes are 鈥渇rozen out.鈥� Also, assume that the only type of work done on the gas is quasistatic compression-expansion work.

  1. For each of the four steps A through D, compute the work done on the gas, the heat added to the gas, and the change in the energy content of the gas. Express all answers in terms of P1, P2, V1, and V2. (Hint: Compute role="math" localid="1651641251162" 螖Ubefore Q, using the ideal gas law and the equipartition theorem.)
  2. Describe in words what is physically being done during each of the four steps; for example, during step A, heat is added to the gas (from an external flame or something) while the piston is held fixed.
  3. Compute the net work done on the gas, the net heat added to the gas, and the net change in the energy of the gas during the entire cycle. Are the results as you expected? Explain briefly.

By applying a pressure of 200atm, you can compress water to 99%of its usual volume. Sketch this process (not necessarily to scale) on aPV diagram, and estimate the work required to compress a liter of water by this amount. Does the result surprise you?

Your 200gcup of tea is boiling-hot. About how much ice should you add to bring it down to a comfortable sipping temperature of 65鈭�C? (Assume that the ice is initially at -15鈭�C. The specific heat capacity of ice is (0.5cal/g鈰�鈭�C..)
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