Ch. 20 - Second Law of Thermodynamics

Giancoli Douglas - Physics for Scientists and Engineers 5th edition

Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Not the one you use?Change textbook

Giancoli Douglas 5th edition

Ch. 20 - Second Law of Thermodynamics

Problem 62b

Chapter 20, Problem 62b

(II) Calculate the probabilities, when you throw two dice, of obtaining an 11.

Verified step by step guidance

Understand the problem: We are calculating the probability of obtaining a sum of 11 when two dice are thrown. Each die has 6 faces, numbered 1 through 6, and the outcomes are independent of each other.

List all possible outcomes: When two dice are thrown, the total number of outcomes is 6 × 6 = 36, since each die has 6 faces and the outcomes are independent.

Identify the favorable outcomes: To get a sum of 11, the possible pairs of numbers on the two dice are (5,6) and (6,5). These are the only combinations that add up to 11.

Count the favorable outcomes: There are 2 favorable outcomes (5,6) and (6,5).

Calculate the probability: The probability is the ratio of favorable outcomes to total outcomes. Use the formula P = (Number of favorable outcomes) / (Total number of outcomes). Substituting the values, P = 2 / 36. Simplify the fraction to get the final probability.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Probability

Probability is a measure of the likelihood of an event occurring, expressed as a ratio of favorable outcomes to the total number of possible outcomes. In the context of rolling dice, it quantifies how likely it is to achieve a specific sum when two dice are thrown.

Sample Space

The sample space is the set of all possible outcomes of a random experiment. For two six-sided dice, the sample space consists of 36 outcomes, represented as ordered pairs (d1, d2), where d1 and d2 can each take values from 1 to 6.

Combinations of Dice Rolls

When rolling two dice, certain combinations yield the same sum. For example, to achieve a total of 11, the combinations are (5,6) and (6,5). Understanding these combinations is essential for calculating the probability of obtaining a specific sum.

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Textbook Question

Suppose that you repeatedly shake six coins in your hand and drop them on the floor. Construct a table showing the number of microstates that correspond to each macrostate. What is the probability of obtaining six heads?

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Textbook Question

Refrigeration units can be rated in “tons.” A 1-ton air conditioning system can remove sufficient energy to freeze 1 ton (2000 pounds = 909 kg) of 0°C water into 0°C ice in one 24-h day. Assume the hot part of a day averages 35°C and the interior of a house is maintained at 22°C by the continuous operation of a 6-ton air conditioning system for 6 hours a day. How much does this cooling cost the homeowner per day, and per month?Assume the work done by the refrigeration unit is powered by electricity that costs \$0.13 per kWh and that the unit’s coefficient of performance is only 18% of an ideal refrigerator. 1 kWh = 3.60 x 10⁶ J .

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Textbook Question

(II) Calculate the probabilities, when you throw two dice, of obtaining a 7.

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Textbook Question

1.00 mole of an ideal monatomic gas at STP first undergoes an isothermal expansion so that the volume at b is 2.5 times the volume at a (Fig. 20–25). Next, heat is extracted at a constant volume so that the pressure drops. The gas is then compressed adiabatically back to the original state. Calculate the pressures at b and c.

At a steam power plant, steam engines work in pairs, the heat output of the first one being the approximate heat input of the second. The operating temperatures of the first are 750°C and 440°C, and of the second 415°C and 240°C. If the heat of combustion of coal is 2.8 x 10⁷ J/kg, at what rate must coal be burned if the plant is to put out 950 MW of power? Assume the efficiency of the engines is 65% of the ideal (Carnot) efficiency.

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