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Unformatted text preview: 1 Homework 4 Answer P2.4) A system consisting of 57.5 g of liquid water at 298 K is heated using an immersion heater at a constant pressure of 1.00 bar. If a current of 1.50 A passes through the 10.0-ohm resistor for 150 s, what is the final temperature of the water? The heat capacity for water can be found in Appendix B. The heat produced by the resistor is: i f m p, 2 T T C n t R I q Solving for T f yields: K 312 K mol J 75.291 mol g 8.02 1 g 5 . 57 K 98 2 K mol J 75.291 mol g 8.02 1 g 5 . 57 s 150 Ohm 10 A 1.5 C n T C n t R I T 1 1- 1- 1 1- 1- 2 m p, i m p, 2 f P2.32) Compare the energy of DNA bending calculated in Problem 2.31 to the thermal energy k B T, where k B is Boltzmann’s constant. Assume T = 310. K. Propose a source for the excess energy required to bend the DNA in Problem 2.31. The thermal energy at 310 K is: J 10 278 . 4 K 10 3 K J 10 38 . 1 T k E-21-1-23 B thermal The ratio between the energy from P2.31 and the thermal energy is: 52.6 J 10 278 . 4 J 10 25 . 2 E E 21--19 thermal bend 2 The energy source could be the formation of intermolecular interactions. Q3.3) Refer to Figure 1.7 and explain why ( U / V ) T is generally small for a real gas. The depth of the potential minimum is generally very small. Therefore, it only takes a small amount of energy to separate the atoms or molecules that make up the gas. Q3.6) Why is the equation valid for an ideal gas even if P is not constant in the process? Is this equation also valid for a real gas? Why or why not? It is valid because for an ideal gas, H is a function of T only, and not a function of V or p. The formula is not accurate for a real gas, since H is a weak function of V and p. P3.2) The function f ( x,y ) is given by f ( x,y ) = xy sin 5 x x 2 y ln y 3 e 2 x 2 cos y . Determine f x y , f y x , 2 f x 2 y , 2 f y 2 x , f y f x y x and x f y x y a. Is y f x y x x f y x y ? b. Obtain an expression for the total differential df. y Cos e x 12 lny y x 2 5x Sin y 5x Cos y x 5 x f 2 2x y y Sin e 3 y 2 lny x y x 5x Sin x y f 2 2x 2 2 x 3 y Cos e x 48 y Cos e 12 lny...
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