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Chapter 20: Q3Q (page 603)

A gas, confined to an insulated cylinder, is compressed adiabatically to half its volume. Does the entropy of the gas increase, decrease, or remain unchanged during this process?

Short Answer

Expert verified

The entropy of the gas remains unchanged during adiabatic compression.

Step by step solution

01

The given data

A gas is compressed adiabatically to half its volume in an insulated cylinder, Vf=12Vi.

02

Understanding the concept of entropy change

Entropy change is a phenomenon that quantifies how disorder or randomness has changed in a thermodynamic system. Using the condition for adiabatic processes in the formula for entropy change, we can predict the change in entropy.

Formulae:

The entropy change for a gas, 鈭�S=鈭�ifdQT=QT 鈥�(颈)

03

Calculation of the entropy change in adiabatic expansion

This is an adiabatic compression. Adiabatic is the process in which heat is exchanged by the system with the surrounding or vice versa.

Hence,dQ=0

Thus, using equation (i), we can get the change in entropy during its expansion as follows:鈭�S=0

Therefore, the change in entropy remains unchanged.

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Most popular questions from this chapter

(a) For 1.0molof a monatomic ideal gas taken through the cycle in Figure, whereV1=4.00V0 , what isW/p0V0 as the gas goes from state a to state calong path abc ?(b)What isrole="math" localid="1661581522914" 鈭�Eint/p0V0 in going from bto cand(c)What is鈭�Eint/p0V0 in going through one full cycle?(d)What is鈭�S in going from bto cand(e)What is鈭�Sin going through one full cycle?

Suppose 2.00 molof a diatomic gas is taken reversibly around the cycle shown in the T-S diagram of Fig. 20-35, whereS1=6.00J/KandS2=8.00J/K. The molecules do not rotate or oscillate. What is the energy transferred as heat Qfor (a) path1鈫�2, (b) path2鈫�3, and (c) the full cycle? (d) What is the worxk Wfor the isothermal process? The volume V1 in state 1 is0.200m3. What is the volume in (e) State 2 and (f) state 3? What is the change鈭�Eintfor (g) path1鈫�2, (h) path2鈫�3, and (i) the full cycle? (Hint:(h) can be done with one or two lines of calculation using Module 19-7 or with a page of calculation using Module 19-9.) (j) What is the work Wfor the adiabatic process?

A gas sample undergoes a reversible isothermal expansion. Figure gives the change鈭�Sin entropy of the gas versus the final volumeVfof the gas. The scale of the vertical axis is set by鈭�Ss=64J/K. How many moles are in the sample?

Figure 20-27 shows a reversible cycle through which 1.00 molof a monatomic ideal gas is taken. Assume thatp=2p0,V=2V0,p0=1.01脳105Pa, andV0=0.0225m3. (a) Calculate the work done during the cycle, (b) Calculate the energy added as heat during stroke abc, and (c) Calculate the efficiency of the cycle. (d) What is the efficiency of a Carnot engine operating between the highest and lowest temperatures that occur in the cycle? (e) Is this greater than or less than the efficiency calculated in (c)?

A Carnot engine absorbs 52 kJas heat and exhausts 36 kJas heat in each cycle. (a) Calculate the engine鈥檚 efficiency and (b) Calculate the work done per cycle in kilojoules.
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