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HW3_Answer

# HW3_Answer - Homework 3 Answer(Due Friday P2.3 P2.7 P2.8...

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1 Homework 3 Answer (Due 02/04/2011 Friday) P2.3, P2.7, P2.8, P2.11, P2.16, P2.19, P2.20, P2.21, P2.23, P2.25, P2.26 P2.3) 3.00 moles of an ideal gas are compressed isothermally from 60.0 to 20.0 L using a constant external pressure of 5.00 atm. Calculate q, w, U, and H. The work against a constant pressure: J 10 03 . 2 m 10 60 m 10 20 Pa 101325 5 V p w 4 3 3 3 3 external 0 U and 0 H since 0 T and PV U H J 10 03 . 2 w q 4 P2.7) For 1.00 mol of an ideal gas, P external = P = 200.0 10 3 Pa. The temperature is changed from 100.0°C to 25.0°C, and C V,m = 3/2 R. Calculate q, w, U, and H. J 935 K 373 - K 98 2 mol K J 314472 . 8 mol .0 1 2 3 T C n U 1 - 1 - m V, J 559 1 K 373 - K 98 2 mol K J 314472 . 8 mol .0 1 2 5 T R C n T C n H 1 - 1 - m V, m p, J H 1559 q P J 624 ) 1559 ( ) 935 ( q - U P J J w P2.11) Calculate H and U for the transformation of 1.00 mol of an ideal gas from 27.0°C and 1.00 atm to 327°C and 17.0 atm if C P , m 20.9 0.042 T K in units of J K 1 mol 1 For an ideal gas, H is given by:

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2 K 600 K 300 T T m p, dT K T 0.042 20.9 n dT C n Δ H f i J 10 11.94 J 10 67 5. J 10 6.27 J T 0.021 J K 300 K 600 20.9 Δ H 3 3 3 K 600 K 300 2 J 10 9.45 K 300 K mol J 8.314472 mol 1 J 10 94 . 1 1 Δ T R n Δ H pV Δ Δ H Δ U 3 1 - 1 - 3 P2.12) Calculate w for the adiabatic expansion of 1.00 mol of an ideal gas at an initial pressure of 2.00 bar from an initial temperature of 450. K to a final temperature of 300. K. Write an expression for the work done in the isothermal reversible expansion of the gas at 300. K from an initial pressure of 2.00 bar. What value of the final pressure would give the same value of w as the first part of this problem? Assume that C P,m = 5/2 R. J 10 1.87 K 50 1 mol K J 314472 . 8 mol 2 3 T R C n U w 3 1 - 1 - m p, ad p p ln T R n w f i reversible and T R n w p p ln reversible f i 7497 . 0 K 00 3 mol K J 314472 . 8 mol 1 J 10 1.87 T R n w p p ln 1 - 1 - 3 reversible f i 12 . 2 p p f i i f p p 0.944 2.12 bar P2.15) An ideal gas undergoes an expansion from the initial state described by P i , V i , T to a final state described by P f , V f , T in (a) a process at the constant external pressure P f and (b) in a reversible process. Derive expressions for the largest mass that can be lifted through a height h in the surroundings in these processes.