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# chap 17 - THE THERMAL BEHAVIOR OF MATTER 17 EXERCISES...

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17.1 THE THERMAL BEHAVIOR OF MATTER EXERCISES Section 17.1 Gases 18. The molar volume of an ideal gas at STP for the surface of Mars can be calculated as in Example 17.1. However, expressing the ideal gas law for 1 mole of gas at the surfaces of Mars and Earth as a ratio, PV T MM M EE E // , = and using the previous numerical result, we find VP P T T V ME M M EE = ( / )( / ) ( / . / 10 0070 218 273 22.4 × 10 2 56 3 = mm 33 ). . 19. INTERPRET We are dealing with an ideal gas. We are given the pressure, temperature, and volume, and want to find the number of gas molecules. DEVELOP We shall use the ideal-gas law, pV NkT = , given in Equation 17.1, to find the number of molecules. EVALUATE From Equation 17.1, we have N PV kT == × × () ( . ) (. 180 8 5 10 138 10 3 23 kPa m J/ 3 K K ) . 350 317 10 23 ASSESS One mole has N A 602 10 23 . molecules. Thus, we have about 0.53 mole of molecules in the system. 20. The ideal gas law in terms of the gas constant per mole, Equation 17.2, gives Pn R T V /( . 3 5 mol) (8.314 J/K mol)(123 K)/ m 3 ⋅= × ) . 0 002 1 79 10 6 Pa. (The absolute temperature must be used, but any convenient units for the gas constant can be used, e.g., R . 0 0821 . L atm/K mol. ⋅⋅ Then P =⋅ 3 5 mol)(0.0821 L atm/K mol) (123 K)/ L atm.) () . 21 7 7 = 21. INTERPRET We are dealing with an ideal gas. We want to know how volume changes with temperature. DEVELOP To compare different states of an ideal gas, it is often convenient to express Equation 17.1 as a ratio: NT 11 22 = In this problem, the pressure is constant, and if no gas escapes or enters, then N is also constant. Therefore, the above equation becomes V V T T 1 2 1 2 = where T is in the Kelvin scale. EVALUATE (a) If T 2 100 = C 373 K and T 1 200 = C 473 K then VV V 12 2 473 373 127 = = K K . (b) If TT 2 = , then 2 = . ASSESS The fact that VT ~ for a given mass of ideal gas at constant pressure is known as the law of Charles and Gay-Lussac. 22. (a) From Equation 17.2: V nRT P ( . ) ( ) 2 8 314 250 15 mol J/mol K K at m P a / a t m mL 3 )( . ) .. 1 013 10 274 10 274 5 2 × = 17

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17.2 Chapter 17 (b) The ideal gas law in ratio form (for a fixed quantity of gas, NN 12 = ) gives: T T PV T 2 1 22 11 2 40 0 == , . . or atm 1.5 atm 5 250 333 1 1 V V = () KK 23. INTERPRET We treat air molecules as ideal gas. Given the pressure, temperature, and volume, we want to find the number of air molecules. DEVELOP We shall use the ideal-gas law, pV NkT = , given in Equation 17.1, to find the number of molecules. EVALUATE The number of air molecules is N kT × −− (. 10 10 138 10 10 3 23 Pa m J/K)( 3 273 K) 2.65 10 7 ASSESS One mole has N A 602 10 23 . molecules. Thus, we have about44 10 17 . × mole of molecules in the system. 24. The thermal speed (also called the rms, or root-mean-square speed) is, from Equation 17.4, vk T m th = 3/ , where m is the mass of a molecule. For molecular hydrogen, m < 2u, so v th J/K K kg = × × 3 1 38 10 800 2 1 66 10 23 27 ) ( ) ) . = 316km/s 25. INTERPRET In this problem we want to compare the speeds of two different molecules that are at different temperatures.
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chap 17 - THE THERMAL BEHAVIOR OF MATTER 17 EXERCISES...

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