Physics Ch 5 & 6 Word Problems

While in Europe, a tourist hears on the radio that the temperature that day will reach a high of 12°C. What is this temperature on the Fahrenheit scale?

To convert Celsius to Fahrenheit, use the formula:

F = (C × 9/5) + 32.

So, F = (12 × 9/5) + 32 = 53.6

Thus, 12°C is equivalent to 53.6°F.

A recipe calls for a cake to be baked at 197°C. At what temperature (Fahrenheit) should the oven be set?

To convert Celsius to Fahrenheit, apply the formula:

F = (C × 9/5) + 32.

So, F = (197 × 9/5) + 32 = 386.6

Therefore, 197°C is equivalent to 386.6°F.

Normal room temperature is about 65°F. What is the equivalent temperature on the Celsius scale?

To convert Fahrenheit to Celsius, use the formula:

C = (F - 32) × 5/9

So, C = (65 - 32) x 5/9 = 18.33

Thus, 65°F is approximately 18.3°C.

A college student produces about 120 kcal of heat per hour on the average. What is the rate of energy production in watts?

To convert kilocalories to watts, use the conversion factor where:

1 kcal/h is approximately equal to 1.163 watts

120 × 1.163 = 139.56

Therefore, 120 kcal/h is approximately 139.6 watts.

A pound of body fat stores an amount of chemical energy equivalent to 3500 Cal. When sleeping, the average adult burns or expends about 0.45 Cal/h for every pound of body weight. How many Calories would a 149 lb person burn during 9 hours of sleep? (Note that 1 Cal = 1 kcal.)

To calculate the total calories burned during sleep, multiply the average calorie burn per hour per pound (0.45 Cal/h) by the person's weight (149 lb) and then by the number of hours (9).

So, (0.45 × 149) * 9 = 603.45

Thus, the total calories burned is approximately 603.45 Cal.

On a brisk walk, a person burns about 365 Cal/h. At this rate, how many hours of brisk walking would it take to lose a pound of body fat? (A pound of body fat stores an amount of chemical energy equivalent to 3500 Cal.)

To determine the hours needed to lose a pound of body fat, divide the total calories in a pound (3500 Cal) by the rate of calories burned per hour (365 Cal/h).

So, 3500 / 365 = 9.589

This results in approximately 9.59 hours of brisk walking.

How much heat in kcal must be added to 0.60 kg of water at room temperature (20°C) to raise its temperature to 49°C?

To calculate the heat needed, use the formula:

Q = mcΔT

where m is the mass of water (0.60 kg), c is the specific heat capacity of water (1 kcal/kg°C), and ΔT is the change in temperature (49°C - 20°C).

So, Q = (0.60 × 1) * 29 = 17.4

Thus, the heat added is approximately 17.4 kcal.

How much heat in joules is needed to raise the temperature of 7.0 L of water from 0°C to 87.0°C? (Hint: Recall the original definition of the liter.)

To find the heat in joules required, apply the formula:

Q = mcΔT

where m is the mass of water (7.0 L = 7.0 kg), c is the specific heat capacity (approximately 4.18 kJ/kg°C), and ΔT is the temperature change (87.0°C - 0°C).

So, (7.0 × 4.18) * 87 = 2548.6 kJ

Thus, the total heat needed is approximately 2,580 kJ or 2580000 J.

A periodic wave has a period of 0.45 s. What is the wave frequency?

The wave frequency can be calculated using the formula:

frequency = 1/period.

So, 1/0.45 = 2.22 Hz

Given the period of 0.45 s, the frequency is approximately 2.22 Hz (1/0.45 = 2.22).

What is the period of the wave motion for a wave with a frequency of 0.58 kHz?

The period of a wave can be calculated using the formula:

period = 1/frequency.

So, 1 / 0.58 = 172 ms or 0.00172 s

For a frequency of 0.58 kHz, the period is approximately 1.72 ms (1/0.58 kHz = 0.00172 s).

Waves moving on a lake have a speed of 2.9 m/s and a distance of 1.8 m between adjacent crests. What is the frequency? Find the period of the wave motion.

First, calculate the frequency using the formula:

frequency = speed/wavelength

For a speed of 2.9 m/s and a wavelength of 1.8 m, the frequency is approximately 1.61 Hz (2.9 m/s ÷ 1.8 m). The period is then calculated as period = 1/frequency, which gives approximately 0.62 s.

A sound wave has a frequency of 2012 Hz. What is the distance between crests or compressions of the wave? (Take the speed of sound to be 344 m/s.)

The distance between crests, or wavelength, can be calculated using the formula:

wavelength = speed/frequency

For a frequency of 2012 Hz and a speed of 344 m/s, the wavelength is approximately 0.171 m (344 m/s ÷ 2012 Hz).

Compute the wavelength of the radio waves from the following stations.

(a) an AM station operating at a frequency of 770 kHz

(b) an FM station with a frequency of 97.7 MHz

The wavelength of a wave can be calculated using the formula: wavelength = speed/frequency.

For the AM station at 770 kHz, using the speed of light (approximately 3 x 10^8 m/s), the wavelength is approximately 390.7 m (3 x 10^8 m/s ÷ 770,000 Hz).

For the FM station at 97.7 MHz, the wavelength is approximately 3.07 m (3 x 10^8 m/s ÷ 97,700,000 Hz).

What is the frequency of blue light that has a wavelength of 450 nm?

The frequency of light can be calculated using the formula:

frequency = speed/wavelength

Using the speed of light (approximately 3 x 10^8 m/s) and converting 450 nm to meters (4.5 x 10^-7 m), the frequency is approximately 6.67 x 10^14 Hz or 667000000000000 Hz.

How far does light travel in one year? [This distance is known as a light-year (ly) and is used in measuring astronomical distances.]

A light-year is the distance that light travels in one year in a vacuum, approximately 9.46 trillion kilometers (9460000000000 Km) or about 5.88 trillion miles.

A new jackhammer has a 1/10 reduction in sound intensity level from that of the older model, which was rated at 114 dB. What is the sound intensity level of the new hammer?

The sound intensity level of the new jackhammer can be calculated by reducing the original level by approximately 10 dB.

So, 114 - 10 = 104

Therefore, the sound intensity level of the new jackhammer is about 104 dB.

During a thunderstorm, 4.6 s elapses between observing a lightning flash and hearing the resulting thunder. Approximately how far away in kilometers and miles was the lightning flash? (Assume the speed of sound is 344 m/s.)

The distance to the lightning flash can be calculated using the formula:

distance = speed × time.

1. So, 344 × 4.6 = 1582.4

2. distance = 1582 m

3. Convert to Kilometers: 1.582 Km

4. Convert to miles: 1 Mile = 1609 m.

5. 1582/1609 = 0.984.

In this case, the distance is approximately 1.58 kilometers or about 0.98 miles.

Equal amounts of heat are added to equal masses of aluminum and silver at the same initial temperature. (The specific heat (at 20°C) of aluminum is 0.22 kcal/kg · °C, and the specific heat (at 20°C) of silver is 0.056 kcal/kg · °C.)

Which metal will have the higher final temperature?

How many times greater will that temperature change be than the temperature change of the other metal?

The metal with the lower specific heat capacity, silver, will have a higher final temperature when the same amount of heat is added.

Solve for temperature change: ΔT= Q/mc

So, 0.22/0.056 = 3.928

Thus, the temperature change of aluminum will be approximately 3.93 times less than that of silver.

A sample of neon gas has its volume tripled and its temperature held constant. What will be the new pressure relative to the initial pressure?

According to Boyle's Law, if the volume of a gas is tripled while keeping the temperature constant, the pressure will decrease to one-third of the initial pressure.

Therefore, the new pressure will be one-third of the original pressure. 1/3.

A fire breaks out and increases the Kelvin temperature of a cylinder of compressed gas by a factor of 1.9. What is the final pressure of the gas relative to its initial pressure?

According to Gay-Lussac's law, if the temperature of a gas increases while volume remains constant, the pressure of the gas will also increase.

Therefore, the final pressure will be 1.9 times the initial pressure.

During exercise, a person’s heart rate increases to 120 beats per minute. What are the frequency and period of this vibration in standard units of Hz and seconds?

The frequency can be calculated by dividing the heart rate by 60 seconds, yielding 2 Hz. The period is the inverse of frequency, which is 0.5 seconds.

You have 1.0 kg of ice that is at a temperature of -10°C.  You have a small Sterno can that can generate a total of 40,000 Joules of heat.  The specific heat of water is 4186 J/kg°C while that of ice is 2100 J/kg°C, and the latent heat of fusion for the water-ice transition is 335000 J/kg.

Express all answers in two significant figures. Numerical answers only; do not include units.

How much heat, in kJ, do you use in raising the temperature of the ice to 0°C?

How much heat, in kJ, remains in the can when the temperature of the ice is 0°C?

How much of the ice, in kg, already at 0^oC, can you melt with the remaining fuel in the Sterno can?

To raise the temperature of 1.0 kg of ice from -10°C to 0°C, use the formula Q = mcΔT.

1. Q = 1.0 kg × 2100 J/kg°C × 10°C = 21,000 J = 21 kJ.

Remaining heat in the can:

40 kJ - 21 kJ = 19 kJ

Amount of ice melted:

19 kJ / 335 kJ/kg = 0.057 kg.

How much heat in kcal must be added to 0.20 kg of liquid water at 100°C in order to change it to steam?  Express your answer in 2 significant figures.

The specific heat of liquid water is 1 kcal/kg°C, its latent heat of fusion is 80 kcal/kg, and its latent heat of vaporization is 540 kcal/kg.  

To change 0.20 kg of water at 100°C to steam, you need to apply the latent heat of vaporization. The total heat required is calculated using:

Q = mL, where L is the latent heat of vaporization.