8 worked answers · short steps first, explanations when you need them
Chapter 11 Exercises
Textbook pages 243
Question 1
A geyser heats water at 3.0 L/min from 27°C to 77°C. If the burner fuel releases 4.0×10⁴ J/g, find the fuel consumption rate. Assume water density 1.0 kg/L and no heat loss.
Steps only
Water flow=3.0 kg/min=0.050 kg/s.
Answer
About 0.26 g/s (15.8 g/min).
Question 2
How much heat is needed to warm 2.0×10⁻² kg nitrogen by 45°C at constant pressure? Molecular mass=28 g/mol and R=8.3 J mol⁻¹ K⁻¹.
Steps only
Moles n=20/28=0.714 mol.
Answer
About 9.3×10² J.
Question 3
Explain: (a) Two bodies at T₁ and T₂ do not necessarily settle at their mean temperature. (b) A plant coolant should have high specific heat. (c) Tyre pressure rises during driving. (d) A harbour town has a milder climate than a desert town at the same latitude.
Steps only
(a) Final temperature depends on the masses and heat capacities of both bodies, and on heat lost to the surroundings.
Answer
(a) It depends on heat capacities and heat exchange. (b) It absorbs much heat with a small rise. (c) The air warms in a nearly fixed volume. (d) The sea heats and cools slowly, moderating the climate.
Question 4
Three moles of hydrogen at standard temperature and pressure are compressed adiabatically to half their original volume. By what factor does the pressure increase? Take γ=7/5 for diatomic hydrogen.
Steps only
For an adiabatic process, PVᵞ=constant.
Answer
The pressure increases by a factor of about 2.64.
Question 5
A gas goes adiabatically from state A to B while 22.3 J of work is done on it. For another path from A to B it absorbs 9.35 cal of heat. Find the work done by the gas on this second path. Use 1 cal=4.19 J.
Steps only
Use ΔU=Q−W, where W is work done by the gas.
Answer
The gas does about 16.9 J of work.
Question 6
Two equal-volume cylinders are connected by a stopcock. Cylinder A contains a gas at STP; B is evacuated. The insulated system is opened. Find: (a) final pressure, (b) change in internal energy, (c) temperature change, (d) whether intermediate states lie on the P–V–T surface.
Steps only
(a) The gas expands into twice its initial volume. For an ideal gas, free expansion gives final pressure half the initial pressure: 0.5 atm.
Answer
(a) 0.5 atm. (b) ΔU=0. (c) ΔT=0 for an ideal gas. (d) No; intermediate states are not equilibrium states.
Question 7
A heater supplies energy at 100 W while the system does work at 75 J/s. At what rate is its internal energy changing?
Steps only
First law in rate form: Q̇=Ū̇+Ẇ.
Answer
Internal energy increases at 25 W.
Question 8
A gas goes from D to E along a straight line on a P–V graph, then from E to F at constant pressure. D=(2.0 m³, 600 N/m²), E=(5.0 m³, 300 N/m²), F=(2.0 m³, 300 N/m²). Find total work done by the gas along D→E→F.