- The Gibbs free energy equation is directly related to which of the following?
- Work and time
- Heat and work
- Enthalpy and entropy
- Power and enthalpy
Gibbs free energy ties together enthalpy and entropy:
\(G=H-TS\)
For changes, \(\Delta G=\Delta H – T\Delta S\). At constant \(T,P\), a negative \(\Delta G\) predicts spontaneity.
- Which expression gives the change in Gibbs free energy for a process at constant temperature?
- \(G=H-TS\)
- \(\Delta G=\Delta H-T\Delta S\)
- \(\Delta G=\Delta H-\frac{T}{S}\)
- \(G=H-\frac{T}{S}\)
The definition of the state function is \(G=H-TS\). The process form is \(\Delta G=\Delta H-T\Delta S\).
- Which of the following is the correct expression of Bernoulli’s principle?
- As KE increases, another form of energy must decrease.
- As KE increases, other forms of energy also increase.
- KE remains relatively stable in a closed loop.
- KE has a limited effect upon wavelength.
Bernoulli’s principle says that along a streamline, the sum \(P+\tfrac12\rho v^2+\rho gh\) is constant. If the kinetic term \(\tfrac12\rho v^2\) goes up (faster flow), at least one of the other forms must go down. So “as KE increases, another form of energy must decrease” matches the trade-off.
- Which of the following is the correct expression of the work–energy theorem?
- \(W=\Delta KE\)
- \(W=K-\Delta E\)
- \(W=K\times\Delta E\)
- \(W=\frac{\Delta K}{\Delta E}\)
The work–energy theorem states that the net work done on an object equals the change in its kinetic energy. The other expressions mis-combine quantities and are not physical laws.
- A spring has a spring constant of 120 N per meter. How much potential energy is stored in the spring as it is stretched 0.2 meters?
- 1.2 J
- 2.4 J
- 3.1 J
- 7.4 J
Elastic potential energy in a spring:
\(U=\dfrac12 kx^2=\dfrac12(120)(0.20)^2=\dfrac12(120)(0.04)\) \(=60\times0.04=2.4\ \text{J}\)
- A distance of \(1 \times 10^3 \text{ m}\) separates the charge at the bottom of the cloud and the ground. The electric field intensity between the bottom of the cloud and the ground is \(2 \times 10^4\) N per coulomb. What is the potential difference between the bottom of the cloud and the ground?
- \(1.4 \times 10^4\text{ V}\)
- \(2.5 \times 10^3\text{ V}\)
- \(2.8 \times 10^6\text{ V}\)
- \(2 \times 10^7\text{ V}\)
For a uniform field, potential difference is \(\Delta V=Ed\).
\(E=2\times10^4\ \text{N/C}\)
\(d=1\times10^3\ \text{m}\)
\(\Delta V=(2\times10^4)(1\times10^3)=2\times10^7\ \text{V}\)
- When Adam drinks cold water, his body warms the water until thermal equilibrium is reached. If he drinks six glasses (2.5 kilograms) of water at 0°C in a day, approximately how much energy must his body expend to raise the temperature of this water to his body’s temperature of 37°C?
- 210 kJ
- 305 kJ
- 390 kJ
- 414 kJ
Heating water (no phase change):
\(Q=mc\Delta T\)
\(m=2.5\ \text{kg}\)
\(c\approx4.186\times10^3\ \text{J/(kg·°C)}\)
\(\Delta T=37^\circ\text{C}\)
\(Q\approx2.5(4.186\times10^3)(37)\) \(\approx3.87\times10^5\ \text{J}=387\ \text{kJ}\)
\(\approx 390 \text{ kJ}\)
- An electron is located between a pair of oppositely charged parallel plates. As the electron approaches the positively charged plate, what happens to the kinetic energy of the electron?
- It increases.
- It decreases.
- It remains the same.
- It transforms into potential energy.
As a negative electron moves toward the positive plate, its electric potential energy \(U=qV\) decreases (since \(q\lt0\) and \(V\) increases).
Thus, by energy conservation, its kinetic energy increases.
- If the speed of a moving object is doubled, which quantity also associated with the object must double?
- Momentum
- KE
- Gravitational potential energy
- Acceleration
Momentum is directly proportional to speed. Doubling \(v\) doubles \(p\).
Kinetic energy (\(KE=\tfrac12 mv^2\)) would quadruple, not double. Gravitational PE doesn’t depend on speed, and acceleration isn’t determined by speed alone.
- A 45 kg bicyclist climbs a hill at a constant speed of 2.5 meters per second by applying an average force of 85 N. Approximately how much power does the bicyclist develop?
- 115 W
- 210 W
- 250 W
- 320 W
Power for constant-speed motion under force \(F\) is:
\(P=Fv=(85\ \text{N})(2.5\ \text{m/s})=212.5\ \text{W}\) \(\approx210\ \text{W}\)
- A person kicks in a 4 kg door with 48 N of force, causing the door to accelerate at 12 m/s2. What is the magnitude of the force exerted by the door on the person?
- 24 N
- 35 N
- 42 N
- 48 N
The door’s acceleration confirms the applied force. By Newton’s third law, the door exerts an equal and opposite force of 48 N on the person.
- A 60 kg student running at 3 meters per second has a kinetic energy of…
- 111 J
- 151 J
- 260 J
- 270 J
\(KE=\dfrac12 mv^2=\dfrac12(60)(3^2)=30\times9=270\ \text{J}\)
- How much work is done in moving 5 coulombs of charge against a potential difference of 12 volts?
- 30 J
- 60 J
- 400 J
- 500 J
Electrical work is:
\(W=q\Delta V=(5\ \text{C})(12\ \text{V})=60\ \text{J}\)
- Compared to insulators, metals are better conductors of electricity because metals contain more free…
- Protons
- Electrons
- Neutrons
- Positive ions
Metals conduct well because they have many delocalized (free) electrons in a conduction band. Protons and neutrons are bound in nuclei, and positive ions are not free charge carriers in metallic solids.
- How much time is required for an operating 100 W light bulb to dissipate 10 J of electrical energy?
- 1 second
- 0.1 seconds
- 0.25 seconds
- 200 seconds
Power is energy per time:
\(P=\dfrac{E}{t}\Rightarrow t=\dfrac{E}{P}\) \(=\dfrac{10\ \text{J}}{100\ \text{W}}=0.10\ \text{s}\)