Chapter 18 Hm. 11

Chapter 18 Hm. 11 - Solutions to Homework #11 Chapter 18...

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Solutions to Homework #11 Chapter 18 Picture the Problem : A monatomic gas undergoes a process in which work is done on the gas, resulting in an increase in temperature. During the process heat may enter or leave the gas. Strategy: Combine the change in energy for a monatomic gas ( 29 3 f i 2 U n R T T = - with the First Law of Thermodynamics (equation 18-3) to solve for the heat flow. Solution: Solve equation 18-3 for Q : ( 29 ( 29 ( 29 ( 29 3 f i 2 3 2 560 J 4 mol 8.31 J/ mol K 130 C 5.9 kJ Q W U W n R T T = + ∆ = + - = - + × ° = Insight: It was not necessary to convert the temperature difference from Celsius degrees to kelvins in this problem because temperature differences are the same in both scales. Picture the Problem : A system that is thermally isolated from its surroundings undergoes a process in which its internal energy increases. Strategy: Use the First Law of Thermodynamics to calculate the work done during an adiabatic process ( 0 Q = ). Solution: 1. Solve the First Law for W , setting Q = 0: U Q W W U = - = -∆ 2. (a) Since the internal energy increased ( 0 U ) the work must be negative, which means it is done on the system. 3. (b) Solve numerically: ( 29 670 J 670 J W U = -∆ = - = - Insight: When no heat can enter or leave a system, any change in internal energy is equal to the work done on the system. Picture the Problem : A monatomic ideal gas expands at constant temperature. Strategy: Use the Ideal Gas Law to solve for the constant temperature. Then use equation 18-5 to solve for the work. Solution: 1. (a) Solve the Ideal Gas Law for the temperature: PV PV nRT T nR = = 2. Insert numeric values: ( 29 ( 29 3 3 i f 100 10 Pa 4.00 m 145 mol 8.31 J/ mol K 332 K T T × = = × = 3. (b) Write equation 18-5, ( 29 3 3 f f i i 3 i i 4.00 m ln ln 400 kPa 1.00 m ln 555 kJ 1.00 m V V W nRT PV V V = = = = ÷ ÷ ÷
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using the ideal gas law to replace nRT PV = : Insight: If the gas had expanded at constant pressure to the same final volume, and then cooled at
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This note was uploaded on 10/17/2011 for the course PHY 101 taught by Professor Ashkenkai during the Fall '08 term at FIU.

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Chapter 18 Hm. 11 - Solutions to Homework #11 Chapter 18...

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