Question

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 change of 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 give 1.00 therm of energy (Assume water forms as a

gas)?

(d) If natural gas costs $0.66 per therm, what is the cost per mole of methane (Assume natural gas is pure

methane)?

(e) How much would it cost to warm 202 gal of water in a hot tub from 15.0°C to 42.0°C? (1 gal = 3.78 L) (d of H₂O = 1.00 g/mL)

For answers (a), (b), and (c) enter your answers in scientific notation.

Answer 1

a)

1 BTU = 1 lb * 1F -->

Q = m * C * dT

dT = 1 F; C = 4.184 JgC; m = 454 g

454 g * 4.184 J/gC * C/1.8F = 1055.2977 J

1 BTU = 1055.2977 J = 1.055*10^3

b)

100000 BTU = x

x = 1055.2977*100000

x = 105529770 J = 1.05529770 *10^8

c)

methane heat combustion = 55.50 kJ/g

105529.770 kJ / 55.50 kJ/g = 1901.43 g of methane

mol = mass/MW = 1901.43/16 = 118.83 mol of methane

1therm = 118.83 mol of methane required = 1.18*10^2 mol

d)

0.66$/therm --> find cost of mol ofmetane

0.66$/therm * 1 therm / 118.83 mol = 0.005554 $ per mol of methane

e)

202 gal of water --> 15°C to 42°C

V =202*3.78 = 763.56 L

m =763.56 kg

Q= m*C*(Tf-Ti)

Q = 763.56*4.184*(42-15) = 86257.8 kJ

1 therm = 1.05529770 *10^8 J

x therm = (86257800)/(1.05529770 *10^8) = 0.8173 therms

$ = 0.66 * 0.8173 = 0.54 $ approx