Ch 19: Work, Heat, and the First Law of Thermodynamics

Knight Calc - Physics for Scientists and Engineers 5th Edition

Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook

Knight Calc 5th Edition

Ch 19: Work, Heat, and the First Law of Thermodynamics

Problem 58

Chapter 19, Problem 58

0.10 mol of nitrogen gas follow the two processes shown in FIGURE P19.58. How much heat is required for each?

Verified step by step guidance

Identify the two processes described in the problem (e.g., isothermal, isochoric, isobaric, or adiabatic) based on the information provided in FIGURE P19.58. Each process will have a specific thermodynamic equation to calculate heat transfer.

For the first process, determine the type of process (e.g., isothermal). If it is isothermal, use the formula for heat transfer:

Q = n R T \ln (V

_fV_i), where

n

is the number of moles,

R

is the gas constant,

T

is the temperature, and

V

_f and

V

_i are the final and initial volumes, respectively.

For the second process, determine the type of process (e.g., isochoric). If it is isochoric, use the formula for heat transfer:

Q = n C

_v⁢∆T, where

C

_v is the molar heat capacity at constant volume and

∆ T

is the change in temperature.

Substitute the given values (e.g.,

n = 0.10

mol, specific temperatures, and volume ratios) into the appropriate formulas for each process. Ensure that the units are consistent (e.g., temperature in Kelvin, volume in cubic meters).

Combine the results from both processes to determine the total heat required. If the problem asks for heat for each process separately, ensure that the calculations for each process are clearly distinguished.

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Key Concepts

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

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. This law is essential for understanding the behavior of gases under various conditions and is crucial for calculating changes in state, such as during heating or cooling processes.

First Law of Thermodynamics

The First Law of Thermodynamics states that energy cannot be created or destroyed, only transformed. It is expressed as ΔU = Q - W, where ΔU is the change in internal energy, Q is the heat added to the system, and W is the work done by the system. This principle is vital for determining the heat required in thermodynamic processes.

Specific Heat Capacity

Specific heat capacity is the amount of heat required to raise the temperature of a unit mass of a substance by one degree Celsius. It varies for different substances and is crucial for calculating the heat transfer involved in temperature changes during the processes described in the question.

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Specific Heat & Temperature Changes

Related Practice

Textbook Question

5.0 g of nitrogen gas at 20°C and an initial pressure of 3.0 atm undergo an isobaric expansion until the volume has tripled. What amount of heat energy is transferred from the gas as its pressure decreases?

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Textbook Question

FIGURE P19.62 shows a thermodynamic process followed by 120 mg of helium. How much heat energy is transferred to or from the gas during each of the three segments?

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Textbook Question

5.0 g of nitrogen gas at 20°C and an initial pressure of 3.0 atm undergo an isobaric expansion until the volume has tripled. How much heat energy is transferred to the gas to cause this expansion?

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Textbook Question

Two cylinders each contain 0.10 mol of a diatomic gas at 300 K and a pressure of 3.0 atm. Cylinder A expands isothermally and cylinder B expands adiabatically until the pressure of each is 1.0 atm. What are the final temperature and volume of each?

Textbook Question

5.0 g of nitrogen gas at 20°C and an initial pressure of 3.0 atm undergo an isobaric expansion until the volume has tripled. What is the gas pressure after the decrease?

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Textbook Question

FIGURE P19.62 shows a thermodynamic process followed by 120 mg of helium. How much work is done on the gas during each of the three segments?

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