Question

1) Lake Erie contains roughly 4.00 ✕ 1011 m3 of water.

(a) How much energy is required to raise the temperature of that volume of water from 17.2°C to 24.8°C? (Assume the density of this water to be equal to that of water at 20°C and 1 atm.)______ J

(b) How many years would it take to supply this amount of energy by using the 1,400-MW exhaust energy of an electric power plant? _____ yr

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2) A 5.80-g lead bullet traveling at 540 m/s is stopped by a large tree. If half the kinetic energy of the bullet is transformed into internal energy and remains with the bullet while the other half is transmitted to the tree, what is the increase in temperature of the bullet? _______ °C

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3) An aluminum cup contains 225 g of water and a 40-g copper stirrer, all at 27°C. A 487-g sample of silver at an initial temperature of 86°C is placed in the water. The stirrer is used to stir the mixture gently until it reaches its final equilibrium temperature of 32°C. Calculate the mass of the aluminum cup. ______g

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4) A(n) 70-g ice cube at 0°C is placed in 670 g of water at 30°C. What is the final temperature of the mixture?
°C

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5) A glass windowpane in a home is 0.62 cm thick and has dimensions of 1.2 m × 2.2 m. On a certain day, the indoor temperature is 20°C and the outdoor temperature is 0°C.

(a) What is the rate at which energy is transferred by heat through the glass?    W

(b) How much energy is lost through the window in one day, assuming the temperatures inside and outside remain constant? J

Answer 1

(1) Density of water at 20C is 998.23 kg/m³

specific heat of water is 4.186 kJ/kgC

mass of the water is 4e11 m³ x 998.23 kg/m³ = 3.993e14 kg

(a) E = cm*dT = 4186 J/kgC x 3.993e14 kg x (24.8 – 17.2)ºC = 1.27 e19 J

(b) 1400-MW = 1.4e9 J/s

1.27 e19 J / 1.4e9 J/s = 9.07 e9 seconds

= (9.07 e9)/(60*60*24*365) yr

= 287.65 yr