ENGG 3260: Thermodynamics
Home Assignment 1 (Chapter 1) (Answer)
1. Why does a bicyclist pick up speed on a downhill road even when he is not pedaling?
Does this violate the conservation of energy principle?
a. On a downhill road the potential energy of the bicyclist is being converted to kinetic
energy, and thus the bicyclist picks up speed.
b. There is no creation of energy, and thus no violation of the conservation of energy
2. An office worker claims that a cup of cold coffee on his table warmed up to 80▯ by
picking up energy from the surrounding air, which is at 25℃. Is there any truth to his
claim? Does this process violate any thermodynamic laws?
a. There is no truth to his claim.
b. It violates the second law of thermodynamics.
3. Determine the mass and the weight of the air contained in a room whose dimensions
are 6 m × 6 m × 8 m. Assume the density of the air is 1.16 kg/m . 3
a. Assumptions: The density of air is constant throughout the room.
b. Properties: The density of air is given to be ρ = 1.16 kg/m .
The mass of the air in the room is
m = ρV = (1.16 kg/m )(6×6×8 m ) = 334.1kg ROOM
2 1 N
W = mg = (334.1kg)(9.81m/s ) 2 = 3277 N
4. A 3-kg rock is thrown upward with a force of 200 N at a location where the local
gravitational acceleration is 9.79 m/s . Determine the acceleration of the rock, in m/s .
a. The weight of the rock is:
W = mg = (3 kg)(9.79 m/s ) = 29.37 N
1kg ⋅/s 2
b. Then the net force that acts on the rock is:
F = F −F = 200−29.37 =170.6 N
net up down
＝＞ From the Newton's second law, the acceleration of the rock becomes
a = F = 170.6 N1kg⋅m/s = 56.9 m/s2
m 3 kg 1 N
5. While solving a problem, a person ends up with the equation E = 25 kJ + 7 kJ/kg at some
stage. Here E is the total energy and has the unit of kilojoules. Determine how to correct
the error and discuss what may have caused it.
The two terms on the right-hand side of the equation
E = 25 kJ + 7 kJ/kg
do not have the same units; therefore, they cannot be added to obtain the total energy.
Multiplying the last term by mass will eliminate the kilograms in the denominator;
moreover, the whole equation will become dimensionally homogeneous.
Every term in the equation will have the same unit.
Discussion Obviously this error was caused by forgetting to multiply the last term by
mass at an earlier stage.
6. A 4-kW resistance heater in a water heater runs for 2 hours to raise the water
temperature to the desired level. Determine the amount of electric energy used in both
kWh and kJ.
The resistance heater consumes electric energy at arate of 4 kW or 4 kJ/s. Then the
total amount of electric energy used in 2 hours becomes
a. Total energy = (Energy per unit time)(Time interval)
= (4 kW)(2 h)
= 8 kWh
b. Noting that 1 kWh = (1 kJ/s)(3600 s) = 3600 kJ,
Total energy = (8 kWh)(3600 kJ/kWh)
= 28,800 kJ
Discussion Note kW is a unit for power whereas kWh is a unit for energy.
7. You have been asked to do a metabolism (energy) analysis of a person. How would you
define the system for this purpose? What type of system is this? Answer:
a. This system is a region of space or open system in that mass such as air and food can
cross its control boundary. The system can also interact with the surroundings by
exchanging heat and work across its control boundary.
b. By tracking these interactions, we can determine the energy conversion
characteristics of this system.
8. You are trying to understand how a reciprocating air compressor (a piston-cylinder
device) works. What system would you use? What type of system is this?