The process abcabc shown in the pVpV-diagram in Fig. E19.1119.11 involves 0.01750.0175 mol of an ideal gas. What was the lowest temperature the gas reached in this process? Where did it occur?

Ch 19: The First Law of Thermodynamics

Young & Freedman Calc - University Physics 14th Edition

Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook

All textbooks

Young & Freedman Calc 14th Edition

Ch 19: The First Law of Thermodynamics

Problem 11a

Chapter 19, Problem 11a

The process $a b c$ shown in the $p V$ -diagram in Fig. E $19.11$ involves $0.0175$ mol of an ideal gas. What was the lowest temperature the gas reached in this process? Where did it occur?

Verified step by step guidance

Identify the points a, b, and c on the pV-diagram. Note the pressure and volume at each point: a (P = 0.20 atm, V = 2.0 L), b (P = 0.60 atm, V = 2.0 L), and c (P = 0.40 atm, V = 6.0 L).

Use the ideal gas law to find the temperature at each point. The ideal gas law is given by:

P V = n R T

, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant (0.0821 L·atm/mol·K), and T is temperature in Kelvin.

Calculate the temperature at point a using the values: P = 0.20 atm, V = 2.0 L, and n = 0.0175 mol. Rearrange the ideal gas law to solve for T:

T = \frac{P V}{n R}

Calculate the temperature at point b using the values: P = 0.60 atm, V = 2.0 L, and n = 0.0175 mol. Use the same rearranged ideal gas law to solve for T.

Calculate the temperature at point c using the values: P = 0.40 atm, V = 6.0 L, and n = 0.0175 mol. Again, use the rearranged ideal gas law to solve for T. Compare the temperatures at points a, b, and c to determine the lowest temperature and identify where it occurs.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

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 (P), volume (V), and temperature (T) of an ideal gas through the equation PV = nRT, where n is the number of moles and R is the ideal gas constant. This law is fundamental for understanding the behavior of gases under various conditions, allowing us to calculate one variable if the others are known.

pV Diagram

A pV diagram is a graphical representation of the relationship between pressure and volume for a gas. In this diagram, different points represent states of the gas, and the paths between these points indicate processes such as isothermal or adiabatic changes. Analyzing the areas and slopes on this diagram helps in understanding work done and heat transfer during gas processes.

Thermodynamic Processes

Thermodynamic processes describe the changes in state variables of a system, such as pressure, volume, and temperature. In the context of the pV diagram, processes can be isothermal (constant temperature), isobaric (constant pressure), or adiabatic (no heat exchange). Identifying the type of process is crucial for determining the lowest temperature reached by the gas during the transition from point a to point c.

Recommended video:

Guided course

08:45

Properties of Cyclic Thermodynamic Processes

Related Practice

Textbook Question

Five moles of an ideal monatomic gas with an initial temperature of $127$ °C expand and, in the process, absorb $1500$ J of heat and do $2100$ J of work. What is the final temperature of the gas?

2210

views

Textbook Question

A gas in a cylinder is held at a constant pressure of $1.80 \times 10^{5}$ Pa and is cooled and compressed from $1.70$ m³ to $1.20$ m³. The internal energy of the gas decreases by $1.40 \times 10^{5}$ J. Does it matter whether the gas is ideal? Why or why not?

1730

views

Textbook Question

A gas in a cylinder expands from a volume of $0.110$ m³ to $0.320$ m³ . Heat flows into the gas just rapidly enough to keep the pressure constant at $1.65 \times 10^{5}$ Pa during the expansion. The total heat added is $1.15 \times 10^{5}$ J. Find the work done by the gas.

1752

views

Textbook Question

The $p V$ -diagram in Fig. E $19.13$ shows a process $a b c$ involving $0.450$ mol of an ideal gas. How much heat had to be added during the process to increase the internal energy of the gas by $15 comma 000$ J?

2232

views

Textbook Question

Figure E $19.8$ shows a $p V$ -diagram for an ideal gas in which its absolute temperature at $b$ is one-fourth of its absolute temperature at $a$ . Did heat enter or leave the gas from $a$ to $b$ ? How do you know?

2562

views

Textbook Question

When water is boiled at a pressure of $2.00$ atm, the heat of vaporization is $2.20 \times 10^{6}$ J/kg and the boiling point is $120$ °C. At this pressure, $1.00$ kg of water has a volume of $1.00 \times 10^{- 3}$ m³, and $1.00$ kg of steam has a volume of $0.824$ m³. Compute the work done when $1.00$ kg of steam is formed at this temperature.

4116

views