Question 1

A block of mass $$m is $$attached to a spring with spring constant $$k$$ and oscillates on a frictionless horizontal surface. If the amplitude of oscillation is doubled, what happens to the period of oscillation?

Accepted Answer

The period remains unchanged.

Question 2

A simple pendulum of length $$L is $$taken from Earth to the Moon, where the acceleration due to gravity is $$g_{moon} = 1.62\ \mathrm{m/s^2$}. If $$its period on Earth is $$T_{earth}$$, what is its period on the Moon?

Accepted Answer

$$T_{moon} = T_{earth} \sqrt{\dfrac{g_{earth}}{g_{moon}}}$$

Question 3

Which of the following best describes the energy transformation in a damped harmonic oscillator?

Accepted Answer

Mechanical energy is gradually converted into thermal energy due to non-conservative forces.

Question 4

A steel bridge expands $$2.4\ \mathrm{cm} in $$length during a hot summer day. If the coefficient of linear expansion for steel is $$\alpha = 1.2 	imes 10$$^{-5}$$\ \mathrm{K$$^{-1}$$}$$ and the temperature change is $$40\ ^\circ\mathrm{C}$$, what is the original length of the bridge?

Accepted Answer

$$L_0$$ = \dfrac{\Delta L}{\alpha \Delta T} = \dfrac{0.024}{1.2 	imes $$10^{-5}$$ 	imes 40} = 50\ \mathrm{m}$$

Question 5

A $$0.5\ \mathrm{kg}$$ block of ice at $$0^\circ\mathrm{C} is $$placed in $$1.0\ \mathrm{kg} of $$water at $$20^\circ\mathrm{C}. $$What is the final temperature after thermal equilibrium is reached? (Assume no heat loss to the environment. $$c_{water} = 4186\ \mathrm{J/kg\cdot K}$$, $$L_f = 3.34 	imes 10^5$\ \mathrm{J/kg})$$

Accepted Answer

The final temperature is $$0^\circ\mathrm{C}$$; not all the ice melts.

Question 6

Which of the following statements about the Kelvin temperature scale is correct?

Accepted Answer

Zero Kelvin is the temperature at which all molecular motion ceases.

Question 7

A gas undergoes an isothermal expansion at temperature $$T. $$According to the first law of thermodynamics, which of the following is true?

Accepted Answer

$$\Delta U = 0$$, so $$Q = W$$

Question 8

A refrigerator removes $$500\ \mathrm{J} of $$heat from its interior and expels $$600\ \mathrm{J} to $$the kitchen. What is the work input required for this process?

Accepted Answer

$$W = Q_H - Q_C = 600\ \mathrm{J} - 500\ \mathrm{J} = 100\ \mathrm{J}$$

Question 9

Which of the following processes increases the entropy of the universe?

Accepted Answer

A hot object cooling down in a cold room.

Question 10

A heat engine absorbs $$2000\ \mathrm{J} of $$heat from a hot reservoir and expels $$1500\ \mathrm{J} to a $$cold reservoir in each cycle. What is its thermal efficiency?

Accepted Answer

$$e = \dfrac{W}{Q_H} = \dfrac{Q_H - Q_C}{Q_H} = \dfrac{2000 - 1500}{2000} = 0.25$$

Question 11

A $$2.0\ \mathrm{kg}$$ block is attached to a vertical spring with $$k = 800\ \mathrm{N/m}. $$What is the period of oscillation?

Accepted Answer

$$T = 2\pi \sqrt{\dfrac{m}{k}} = 2\pi \sqrt{\dfrac{2.0}{800}} \approx 0.314\ \mathrm{s}$$

Question 12

Which of the following is NOT a condition for simple harmonic motion (SHM)?

Accepted Answer

The acceleration is always constant.

Question 13

A $$1.0\ \mathrm{mol}$$ sample of an ideal gas at $$300\ \mathrm{K} is $$heated at constant volume until its temperature reaches $$600\ \mathrm{K}. By $$what factor does its pressure increase?

Accepted Answer

The pressure doubles.

Question 14

Which of the following best describes the physical meaning of entropy?

Accepted Answer

Entropy measures the degree of disorder or randomness in a system.

Question 15

A $$0.2\ \mathrm{kg}$$ copper rod ($$c = 386\ \mathrm{J/kg\cdot K}) at$$ $$100^\circ\mathrm{C} is $$placed in $$0.5\ \mathrm{kg} of $$water at $$20^\circ\mathrm{C}. $$What is the final equilibrium temperature? (Assume no heat loss to the environment.)

Accepted Answer

The final temperature is between $$20^\circ\mathrm{C}$$ and $$100^\circ\mathrm{C}$$, found by solving $$m_{Cu}c$$_{Cu}(T_f - 100) + $$m_{w}c$$_{w}(T_f - 20) = 0$$.

Question 16

Which of the following is a correct statement of the second law of thermodynamics?

Accepted Answer

No heat engine operating between two heat reservoirs can be more efficient than a Carnot engine.

Question 17

A $$0.1\ \mathrm{kg}$$ aluminum plate ($$c = 900\ \mathrm{J/kg\cdot K}) at$$ $$150^\circ\mathrm{C} is $$dropped into $$0.5\ \mathrm{kg} of $$water at $$25^\circ\mathrm{C}. $$What is the direction of heat flow?

Accepted Answer

Heat flows from the aluminum plate to the water.

Question 18

A Carnot engine operates between $$T_H = 500\ \mathrm{K}$$ and $$T_C = 300\ \mathrm{K}. $$What is its maximum possible efficiency?

Accepted Answer

$$e_{max} = 1 - \dfrac{T_C}{T_H} = 1 - \dfrac{300}{500} = 0.4$$

Question 19

Which of the following is true for an adiabatic process involving an ideal gas?

Accepted Answer

No heat is exchanged with the surroundings: $$Q = 0.$$

Question 20

A physical pendulum consists of a uniform rod of length $$L$$ and mass $$M$$ pivoted at one end. What is the period of small oscillations?

Accepted Answer

$$T = 2\pi \sqrt{\dfrac{2L}{3g}}$$

PHY 251 Exam 4 Study Guide: Oscillations and Thermodynamics

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