Chapter 1, Problem 1.4E

The calorie (4.184 J) was originally defined as the quantity of energy required to raise the temperature of 1.00 g of liquid water 1.00°C. The British thermal unit (Btu) is defined as the quantity of energy required to raise the temperature of 1.00 lb of liquid water 1.00°F.(a) How many joules are in 1.00 Btu (1 lb 453.6 g; a changeof 1.0°C= 1.8°F)?(b) The therm is a unit of energy consumption and is defined as 100,000 Btu. How many joules are in 1.00 therm?(c) How many moles of methane must be burned to give1.00 therm of energy? (Assume water forms as a gas.)(d) If natural gas costs $0.66 per therm, what is the cost per moleof methane? (Assume natural gas is pure methane.)(e) How much would it cost to warm 318 gal of water in a hottub from 15.0°C to 42.0°C (1 gal 3.78 L)?

When organic matter decomposes under oxygen-free (anaerobic) conditions, methane is one of the products. Thus, enormous deposits of natural gas, which is almost entirely methane, serve as a major source of fuel for home and industry.(a) Known deposits of natural gas can produce 5600 EJ of energy (1 EJ = 1018 J). Current total global energy usage is 4.0×102 EJ per year. Find the mass (in kg) of known deposits of natural gas (ΔH°rxn for the combustion of CH4 = -802 kJ/mol).(b) At current rates of usage, for how many years could these deposits supply the world’s total energy needs?(c) What volume (in ft3) of natural gas, measured at STP, is required to heat 1.00 qt of water from 25.0°C to 100.0°C (d of H2O = 1.00 g/mL; d of CH4 at STP = 0.72 g/L)?(d) The fission of 1 mol of uranium (about 4×10-4 ft3) in a nuclear reactor produces 2×1013 J. What volume (in ft3) of natural gas would produce the same amount of energy?

1.42 (a) and (b)