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When a dilute gas expands quasi-statically from 0.50 to 4.0 L, it does 250 J of work. Assuming that the gas temperature remains constant at 300 K, (a) what is the change in the internal energy of the gas? (b) How much heat is absorbed by the gas in this process?

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In a quasi-static isobaric expansion, 500 J of work are done by the gas. The gas pressure is 0.80 atm and it was originally at 20.0 L. If the internal energy of the gas increased by 80 J in the expansion, how much heat does the gas absorb?

580 J

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An ideal gas expands quasi-statically and isothermally from a state with pressure p and volume V to a state with volume 4V. How much heat is added to the expanding gas?

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As shown below, if the heat absorbed by the gas along AB is 400 J, determine the quantities of heat absorbed along (a) ADB; (b) ACB; and (c) ADCB.

The figure is a plot of pressure, p, in atmospheres on the vertical axis as a function of volume, V, in Liters on the horizontal axis. The horizontal volume scale runs from 0 to 5.0 Liters, and the vertical pressure scale runs from 0 to 4.0 atmospheres. Four points, A, B, C, and D are labeled. Point A is at 1.0 L, 1.0 atmospheres. Point B is at 3.0 L, 1.0 atmospheres. Point C is at 3.0 L, 2.0 atmospheres. Point D is at 1.0 L, 3.0 atmospheres. A straight horizontal line connects A to B, with an arrow pointing to the right indicating the direction from A to B. A straight horizontal line connects D to C, with an arrow to the right indicating the direction from D to C. A straight vertical line connects A to D, with an arrow pointing upward indicating the direction from A to D. A straight vertical line connects C to B, with an arrow downward indicating the direction from C to B. Finally, a straight diagonal line connects D to B with an arrow pointing in the direction from D to B.

a. 600 J; b. 600 J; c. 800 J

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During the isobaric expansion from A to B represented below, 130 J of heat are removed from the gas. What is the change in its internal energy?

The figure is a plot of pressure, p, in Newtons per square meter on the vertical axis as a function of volume, V, in cubic meters on the horizontal axis. The horizontal volume scale runs from 0 to 3.0 cubic meters, and the vertical pressure scale is labeled at only one pressure, 1.0 times 10 to the 4 Newtons per square meter. Two points, A and B, are labeled, both at the labeled pressure of 1.0 times 10 to the 4 Newtons per square meter. Point A is at 0.15 cubic meters. Point B is at 0.3 cubic meters. A horizontal line connects A to B, with an arrow pointing to the right, from A to B.
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(a) What is the change in internal energy for the process represented by the closed path shown below? (b) How much heat is exchanged? (c) If the path is traversed in the opposite direction, how much heat is exchanged?

The figure is a plot of pressure, p, in atmospheres on the vertical axis as a function of volume, V, in Liters on the horizontal axis. The horizontal volume scale runs from 0 to 5.0 Liters, and the vertical pressure scale runs from 0 to 4.0 atmospheres. Two points, R and S, are labeled. Point R is at 1.0 L, 1.0 atmospheres. Point S is at 3.0 L, 1.0 atmospheres. A semicircle goes up from R and over to S, with an arrow showing the clockwise direction on the curve. A horizontal line returns, with an arrow pointing to the left, from S to R.

a. 0; b. 160 J; c. –160 J

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When a gas expands along path AC shown below, it does 400 J of work and absorbs either 200 or 400 J of heat. (a) Suppose you are told that along path ABC, the gas absorbs either 200 or 400 J of heat. Which of these values is correct? (b) Give the correct answer from part (a), how much work is done by the gas along ABC? (c) Along CD, the internal energy of the gas decreases by 50 J. How much heat is exchanged by the gas along this path?

The figure is a plot of pressure, p on the vertical axis as a function of volume, V on the horizontal axis. Four points, A, B, C, and D are shown. B is directly above A, at the same volume but with p B greater than p A. Likewise, C is directly above D, at the same volume but with p C greater than p D.   A and D are at the same pressure, with p D greater than p A. B and C are at the same pressure, with p C greater than p B. Four paths are shown. One path connects from A straight up to B. One path connects from B horizontally to the right to C. One path connects from C straight down to D. And the last path connects from A to C with a somewhat wavy curve that remains above the A D pressure and below the B C pressure.
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When a gas expands along AB (see below), it does 500 J of work and absorbs 250 J of heat. When the gas expands along AC , it does 700 J of work and absorbs 300 J of heat. (a) How much heat does the gas exchange along BC ? (b) When the gas makes the transmission from C to A along CDA , 800 J of work are done on it from C to D . How much heat does it exchange along CDA ?

The figure is a plot of pressure, p on the vertical axis as a function of volume, V on the horizontal axis. Four points, A, B, C, and D are shown. B is directly above A, at the same volume but with p B greater than p A. Likewise, C is directly above D, at the same volume but with p C greater than p D.   A and D are at the same pressure, with p D greater than p A. B and C are at the same pressure, with p C greater than p B. Five paths are shown. Four form a rectangle with the arrows indicating traversing it in a counter clockwise direction.  One path connects from A horizontally to the right to B. The next path connects from B vertically up to C. The next path connects from C horizontally to the left to D. The next path connects from D vertically back down to A. The fifth path connects from A to C with a somewhat wavy curve that remains inside the rectangle.

a. –150 J; b. –400 J

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A dilute gas is stored in the left chamber of a container whose walls are perfectly insulating (see below), and the right chamber is evacuated. When the partition is removed, the gas expands and fills the entire container. Calculate the work done by the gas. Does the internal energy of the gas change in this process?

The figure is an illustration of a container with a partition in the middle dividing it into two chambers.  The outer walls are insulated. The chamber on the left is full of gas, indicated by blue shading and many small dots representing the gas molecules. The right chamber is empty.
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Ideal gases A and B are stored in the left and right chambers of an insulated container, as shown below. The partition is removed and the gases mix. Is any work done in this process? If the temperatures of A and B are initially equal, what happens to their common temperature after they are mixed?

The figure is an illustration of a container with a partition in the middle dividing it into two chambers.  The outer walls are insulated.The chamber on the left is labeled with an A, and is full of one gas, indicated by blue shading and many small dots representing the gas molecules. The right chamber is labeled with a B, and is full of a second gas, indicated by red shading and many small dots representing the gas molecules.

No work is done and they reach the same common temperature.

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An ideal monatomic gas at a pressure of 2.0 × 10 5 N/m 2 and a temperature of 300 K undergoes a quasi-static isobaric expansion from 2.0 × 10 3 to 4.0 × 10 3 cm 3 . (a) What is the work done by the gas? (b) What is the temperature of the gas after the expansion? (c) How many moles of gas are there? (d) What is the change in internal energy of the gas? (e) How much heat is added to the gas?

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Consider the process for steam in a cylinder shown below. Suppose the change in the internal energy in this process is 30 kJ. Find the heat entering the system.

The figure is a plot of pressure, p in atmospheres, on the vertical axis as a function of volume, V in Liters, on the horizontal axis. The horizontal volume scale runs from 0 to 12. The vertical pressure scale runs from 0 to 50. A straight line with negative slope is shown, with an arrow pointing down and to the left. The line extends from volume of 5 Liters, pressure of 50 atmospheres to volume of 12 Liters, pressure of 20 atmospheres.

54,500 J

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The state of 30 moles of steam in a cylinder is changed in a cyclic manner from a-b-c-a, where the pressure and volume of the states are: a (30 atm, 20 L), b (50 atm, 20 L), and c (50 atm, 45 L). Assume each change takes place along the line connecting the initial and final states in the pV plane. (a) Display the cycle in the pV plane. (b) Find the net work done by the steam in one cycle. (c) Find the net amount of heat flow in the steam over the course of one cycle.

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A monatomic ideal gas undergoes a quasi-static process that is described by the function p ( V ) = p 1 + 3 ( V V 1 ) , where the starting state is ( p 1 , V 1 ) and the final state ( p 2 , V 2 ) . Assume the system consists of n moles of the gas in a container that can exchange heat with the environment and whose volume can change freely. (a) Evaluate the work done by the gas during the change in the state. (b) Find the change in internal energy of the gas. (c) Find the heat input to the gas during the change. (d) What are initial and final temperatures?

a. ( p 1 + 3 V 1 2 ) ( V 2 V 1 ) 3 V 1 ( V 2 2 V 1 2 ) + ( V 2 3 V 1 3 ) ; b. 3 2 ( p 2 V 2 p 1 V 1 ) ; c. the sum of parts (a) and (b); d. T 1 = p 1 V 1 n R and T 2 = p 2 V 2 n R

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A metallic container of fixed volume of 2.5 × 10 −3 m 3 immersed in a large tank of temperature 27 ° C contains two compartments separated by a freely movable wall. Initially, the wall is kept in place by a stopper so that there are 0.02 mol of the nitrogen gas on one side and 0.03 mol of the oxygen gas on the other side, each occupying half the volume. When the stopper is removed, the wall moves and comes to a final position. The movement of the wall is controlled so that the wall moves in infinitesimal quasi-static steps. (a) Find the final volumes of the two sides assuming the ideal gas behavior for the two gases. (b) How much work does each gas do on the other? (c) What is the change in the internal energy of each gas? (d) Find the amount of heat that enters or leaves each gas.

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A gas in a cylindrical closed container is adiabatically and quasi-statically expanded from a state A (3 MPa, 2 L) to a state B with volume of 6 L along the path 1.8 p V = constant . (a) Plot the path in the pV plane. (b) Find the amount of work done by the gas and the change in the internal energy of the gas during the process.

a.
The figure is a plot of pressure, p in MegaPascals, on the vertical axis as a function of volume, V in Liters, on the horizontal axis. The horizontal volume scale runs from 0 to 6. The vertical pressure scale runs from 0 to 3. Two points, A at 2 Liters, 3 MegaPascals, and B at 6 Liters, and an unlabeled pressure, are shown and are connected by a curve. The curve is monotonically decreasing and concave up. ;
b. W = 4.39 kJ, Δ E int = −4.39 kJ

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Source:  OpenStax, University physics volume 2. OpenStax CNX. Oct 06, 2016 Download for free at http://cnx.org/content/col12074/1.3
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