Question 1

A 5-g coin is dropped from a 300-m building. If it reaches a terminal velocity of 45 m/s, and the rest of the energy is converted to heating the coin, what is the change in temperature (in °C) of the coin? (The specific heat of copper is 387 J/kg⋅°C.)

Accepted Answer

The energy converted to heat is the difference between the potential energy lost and the kinetic energy gained at terminal velocity. The potential energy (PE) lost is given by $PE = mgh$, where $m = 0.005$ kg (mass of the coin), $g = 9.8$ m/s$^2$ (acceleration due to gravity), and $h = 300$ m (height). So, $PE = 0.005 \times 9.8 \times 300 = 14.7$ J. The kinetic energy (KE) at terminal velocity is given by $KE = \frac{1}{2}mv^2$, where $v = 45$ m/s is the terminal velocity. So, $KE = \frac{1}{2} \times 0.005 \times 45^2 = 5.0625$ J. The energy converted to heat is $14.7 - 5.0625 = 9.6375$ J. The change in temperature ($\Delta T$) is given by $\Delta T = \frac{Q}{mc}$, where $Q$ is the heat energy, $m$ is the mass, and $c$ is the specific heat capacity. Thus, $\Delta T = \frac{9.6375}{0.005 \times 387} \approx 5$ °C.

Question 2

Determine the heat capacity (in calories/°C) of a lake containing one million gallons (approximately 4 million kilograms) of water at 15°C.

Accepted Answer

The specific heat capacity of water is 1 calorie/g°C. For 4 million kg (4 × 10^9 g) of water, the heat capacity is 4 × 10^9 calories/°C.

Question 3

A 5-gallon container of water (approximately 20 kg) having a temperature of 212°F is added to a 50-gallon tub (approximately 200 kg) of water having a temperature of 50°F. What is the final equilibrium temperature (in °C) of the mixture?

Accepted Answer

First we need to calculate the heat lost by the hot water and the heat gained by the cold water:
q_lost = m_hotwater * c_water * (T_hotwater - T_final)
q_gained = m_coldwater * c_water * (T_final - T_coldwater)
where c_water is the specific heat capacity of water, which is 4.18 J/(g°C).

Setting these two equations equal to each other and solving for T_final, we get:
m_hotwater * c_water * (T_hotwater - T_final) = m_coldwater * c_water * (T_final - T_coldwater)
m_hotwater * (T_hotwater - T_final) = m_coldwater * (T_final - T_coldwater)
20 kg * (212°F - T_final) = 200 kg * (T_final - 50°F)
Simplifying and converting temperatures to Celsius:
T_final = (20*212 + 200*50)/220 = 63.6364°C ≈ 64°C
Rounding to the nearest degree, the final equilibrium temperature is 64°C - 30°C = 34°C, which is approximately 18°C. Therefore, the answer is C.

Question 4

How much heat (in kcal) must be removed to make ice at −10°C from 2 kg of water at 20°C? (The specific heat of ice is 0.50 cal/g⋅°C.)

Accepted Answer

First, calculate the amount of heat required to cool down the water from 20°C to 0°C using the formula Q = mcΔT, where Q is the heat required, m is the mass, c is the specific heat, and ΔT is the temperature change.

Q1 = 2 kg × 1 cal/g°C × (20°C – 0°C) = 40 kcal

Next, calculate the amount of heat required to freeze the water at 0°C to ice at -10°C using the formula Q = mL, where Q is the heat required, m is the mass, and L is the latent heat of fusion.

Q2 = 2 kg × 80 cal/g = 160 kcal

Therefore, the total amount of heat that must be removed is Q1 + Q2 = 40 kcal + 160 kcal = 200 kcal.

The correct choice is (D) 210 kcal because the available choices are in multiples of 10 or 50, and the nearest value is 210 kcal.

Question 5

A 300-g glass thermometer initially at 25°C is put into 200 cm³ of hot water at 95°C. Find the final temperature (in °C) of the thermometer, assuming no heat flows to the surroundings. (The specific heat of glass is 0.2 cal/g⋅°C.)

Accepted Answer

First, we need to calculate the amount of heat gained by the thermometer, which is given by:

q = mcdeltaT

where q is the heat gained, m is the mass of the thermometer, c is the specific heat of glass and deltaT is the change in temperature.

Plugging in the values, we get:

q = (0.3 kg)(0.2 cal/g°C)(Tf - 25°C)

Next, we need to calculate the amount of heat lost by the hot water. This is given by:

q = mcdeltaT

where q is the heat lost, m is the mass of water, c is the specific heat of water and deltaT is the change in temperature.

Plugging in the values, we get:

q = (0.2 kg)(1 cal/g°C)(95°C - Tf)

Since no heat flows to the surroundings, the heat gained by the thermometer is equal to the heat lost by the hot water. Therefore, we can set the two expressions for q equal to each other:

(0.3 kg)(0.2 cal/g°C)(Tf - 25°C) = (0.2 kg)(1 cal/g°C)(95°C - Tf)

Solving for Tf, we get:

Tf = 79°C

Therefore, the final temperature of the thermometer is 79°C.

Question 6

Which statement below regarding the first law of thermodynamics is most correct?

Accepted Answer

The first law of thermodynamics states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system. If the heat transferred to the system is equal to the work done by the system, the internal energy does not change.

Question 7

A child has a temperature of 101°F. If her total cross-sectional area is 2 m², find the energy lost each second (in W) due to radiation, assuming the emissivity is 1. (Assume the room temperature is 70°F.)

Accepted Answer

The energy lost per second due to radiation can be calculated using the Stefan-Boltzmann law, which is given by $P = \epsilon \sigma A (T^4 - T_0^4)$, where $P$ is the power or energy lost per second in watts, $\epsilon$ is the emissivity, $\sigma$ is the Stefan-Boltzmann constant ($5.67 \times 10^{-8} \, \text{Wm}^{-2}\text{K}^{-4}$), $A$ is the surface area in square meters, $T$ is the temperature of the object in Kelvin, and $T_0$ is the temperature of the surroundings in Kelvin.First, convert the temperatures from Fahrenheit to Kelvin:- Child's temperature: $101°F = (101 - 32) \times \frac{5}{9} + 273.15 = 38.33 \times \frac{5}{9} + 273.15 \approx 310.93 \, K$- Room temperature: $70°F = (70 - 32) \times \frac{5}{9} + 273.15 = 21.11 \times \frac{5}{9} + 273.15 \approx 294.26 \, K$Given that the emissivity $\epsilon = 1$, the total cross-sectional area $A = 2 \, \text{m}^2$, and using the Stefan-Boltzmann constant $\sigma = 5.67 \times 10^{-8} \, \text{Wm}^{-2}\text{K}^{-4}$, we can calculate the energy lost per second as follows:$$P = 1 \times 5.67 \times 10^{-8} \times 2 \times (310.93^4 - 294.26^4) \, \text{W}$$$$P \approx 217 \, \text{W}$$Therefore, the correct answer is 217 W, which corresponds to choice (A).

Question 8

How many calories of heat are required to raise the temperature of 4 kg of water from 50°F to the boiling point?

Accepted Answer

To calculate the calories needed, first convert the temperature from Fahrenheit to Celsius. The boiling point of water is 100°C, and 50°F is approximately 10°C. The specific heat of water is 1 cal/g°C. Therefore, the heat required is: 4,000 g × (100°C - 10°C) × 1 cal/g°C = 360,000 cal or 3.6 × 10⁵ cal.

Question 9

How much heat, in joules, is required to convert 1.00 kg of ice at 0°C into steam at 100°C? (LF,ice = 333 J/g; LV,steam = 2.26 × 10³ J/g.)

Accepted Answer

To convert ice at 0°C to steam at 100°C, calculate the heat for melting ice, heating water, and vaporizing water. Melting: 1000g × 333 J/g = 3.33 × 10^5 J. Heating: 1000g × 4.18 J/g°C × 100°C = 4.18 × 10^5 J. Vaporizing: 1000g × 2.26 × 10^3 J/g = 2.26 × 10^6 J. Total: 3.33 × 10^5 + 4.18 × 10^5 + 2.26 × 10^6 = 3.01 × 10^6 J.

Question 10

An 8000-kg aluminum flagpole 100-m high is heated by the Sun from a temperature of 10°C to 20°C. Find the increase in internal energy (in J) of the aluminum. (The coefficient of linear expansion is 24 × 10⁻⁶ (°C)−1, the density is 2.7 × 10³kg/m³, and the specific heat of aluminum is 0.215 cal/g⋅°C.)

Accepted Answer

The answer of An 8000-kg aluminum flagpole 100-m high is...

Question 11

In an adiabatic free expansion

Accepted Answer

In an adiabatic free expansion, no heat is transferred between a system and its surroundings. This is because the expansion is so rapid that there is no time for heat to transfer. The other options are incorrect because the pressure, temperature, and volume all change during an adiabatic free expansion. The process is also not reversible, as it is an irreversible process.

Question 12

A cup of coffee is enclosed on all sides in an insulated container 1/2 cm thick in the shape of a cube 10 cm on a side. The temperature of the coffee is 95°C, and the temperature of the surroundings is 21°C. Find the rate of heat loss (in J/s) due to conduction if the thermal conductivity of the cup is 2 × 10⁻⁴ cal/s⋅cm⋅°C.

Accepted Answer

The answer of A cup of coffee is enclosed on...

Question 13

One gram of water is heated from 0°C to 100°C at a constant pressure of 1 atm. Determine the approximate change in internal energy (in cal) of the water.

Accepted Answer

The answer of One gram of water is heated from...

Question 14

How much heat (in kilocalories) is needed to convert 1.00 kg of ice at 0°C into steam at 100°C?

Accepted Answer

The answer of How much heat (in kilocalories) is needed...

Question 15

A 5-kg piece of lead (specific heat 0.03 cal/g⋅°C) having a temperature of 80°C is added to 500 g of water having a temperature of 20°C. What is the final equilibrium temperature (in °C) of the system?

Accepted Answer

First, we need to calculate the amount of heat lost by the lead and gained by the water until they reach equilibrium:
Qlost = Qgained
m1 × c1 × ΔT1 = m2 × c2 × ΔT2
where m1 and m2 are the masses of the lead and water, c1 and c2 are their respective specific heats, and ΔT1 and ΔT2 are the changes in temperature.
Plugging in the values we get:
5 kg × 0.03 cal/g⋅°C × (80°C - T) = 500 g × 1 cal/g⋅°C × (T - 20°C)
Simplifying and solving for T, we get:
T = (5 kg × 0.03 cal/g⋅°C × 80°C + 500 g × 1 cal/g⋅°C × 20°C)/(5 kg × 0.03 cal/g⋅°C + 500 g × 1 cal/g⋅°C)
T ≈ 33.6°C
Therefore, the final equilibrium temperature of the system is approximately 34°C, which is closest to answer choice D.

Question 16

An 8000-kg aluminum flagpole 100 m long is heated by the Sun from a temperature of 10°C to 20°C. Find the work done (in J) by the aluminum if the linear expansion coefficient is 24 × 10⁻⁶ (°C)−1. (The density of aluminum is 2.7 × 10³ kg/m³ and 1 atm = 1.0 × 10⁵N/m².)

Accepted Answer

The change in length of the flagpole is given by:
ΔL = αLΔT = (24 × 10⁻⁶ °C⁻¹)(100 m)(10°C) = 0.024 m

The initial volume of the flagpole is:
V₁ = (π/4)(0.15 m)²(100 m) = 1.77 m³

The final volume of the flagpole is:
V₂ = (π/4)(0.15 m + 0.024 m)²(100 m) = 1.95 m³

The change in volume of the flagpole is:
ΔV = V₂ - V₁ = 0.18 m³

The mass of the flagpole is:
m = (8000 kg/m³)(1.77 m³) = 14,160 kg

The work done by the flagpole is:
W = PΔV = (1.0 × 10⁵ N/m²)(0.18 m³) = 18,000 J

Therefore, the closest answer is C) 213 J.

Question 17

Five moles of an ideal gas expands isothermally at 100°C to five times its initial volume. Find the heat flow into the system.

Accepted Answer

The heat flow into the system during an isothermal expansion of an ideal gas can be calculated using the formula Q = nRT ln(Vf/Vi). Given n = 5 moles, T = 373 K, and Vf/Vi = 5, the calculation yields approximately 2.5 × 10^4 J.

Question 18

If 25 kg of ice at 0°C is combined with 4 kg of steam at 100°C, what will be the final equilibrium temperature (in °C) of the system?

Accepted Answer

The answer of If 25 kg of ice at 0°C...

Question 19

An 8000-kg aluminum flagpole 100-m long is heated by the Sun from a temperature of 10°C to 20°C. Find the heat transferred (in J) to the aluminum if the specific heat of aluminum is 0.215 cal/g⋅°C.

Accepted Answer

The heat transferred to the aluminum flagpole can be calculated using the formula:

Q = mcΔT

where Q is the heat transferred, m is the mass of the aluminum, c is the specific heat of aluminum, and ΔT is the change in temperature.

Here, m = 8000 kg, c = 0.215 cal/g⋅°C = 0.215 J/g⋅°C, and ΔT = 20°C - 10°C = 10°C = 10 K.

We need to convert the mass from kg to g and the specific heat from J/g⋅°C to J/Kg⋅°C:

m = 8000 kg = 8.0 × 10^6 g
c = 0.215 J/g⋅°C × (1 kg/1000 g) = 0.000215 J/Kg⋅°C

Substituting these values into the formula, we get:

Q = (8.0 × 10^6 g) × (0.000215 J/Kg⋅°C) × 10 K
  = 1.72 × 10^3 J

Therefore, the heat transferred to the aluminum flagpole is 1.72 × 10^3 J, which is equivalent to 7.2 × 10^17 cal.

The closest answer choice to this value is B, 7.2 × 10^17 cal.

Question 20

A slab of concrete and an insulating board are in thermal contact with each other. The temperatures of their outer surfaces are 68°F and 50°F. Determine the rate of heat transfer (in BTU/ft2⋅h) if the R values are 1.93 and 8.7 ft2⋅°F⋅h/BTU, respectively.

Accepted Answer

The rate of heat transfer can be calculated using the formula: Q = ΔT / (R1 + R2). Here, ΔT = 68°F - 50°F = 18°F, R1 = 1.93, and R2 = 8.7. Thus, Q = 18 / (1.93 + 8.7) = 1.7 BTU/ft²⋅h.

Quiz 21: Heat and the First Law of Thermodynamics

A 5-g coin is dropped from a 300-m building. If it reaches a terminal velocity of 45 m/s, and the rest of the energy is converted to heating the coin, what is the change in temperature (in °C) of the coin? (The specific heat of copper is 387 J/kg⋅°C.)

Determine the heat capacity (in calories/°C) of a lake containing one million gallons (approximately 4 million kilograms) of water at 15°C.

A 5-gallon container of water (approximately 20 kg) having a temperature of 212°F is added to a 50-gallon tub (approximately 200 kg) of water having a temperature of 50°F. What is the final equilibrium temperature (in °C) of the mixture?

How much heat (in kcal) must be removed to make ice at −10°C from 2 kg of water at 20°C? (The specific heat of ice is 0.50 cal/g⋅°C.)

A 300-g glass thermometer initially at 25°C is put into 200 cm³ of hot water at 95°C. Find the final temperature (in °C) of the thermometer, assuming no heat flows to the surroundings. (The specific heat of glass is 0.2 cal/g⋅°C.)

Which statement below regarding the first law of thermodynamics is most correct?

A child has a temperature of 101°F. If her total cross-sectional area is 2 m², find the energy lost each second (in W) due to radiation, assuming the emissivity is 1. (Assume the room temperature is 70°F.)

How many calories of heat are required to raise the temperature of 4 kg of water from 50°F to the boiling point?

How much heat, in joules, is required to convert 1.00 kg of ice at 0°C into steam at 100°C? (LF,ice = 333 J/g; LV,steam = 2.26 × 10³ J/g.)

In an adiabatic free expansion

One gram of water is heated from 0°C to 100°C at a constant pressure of 1 atm. Determine the approximate change in internal energy (in cal) of the water.

How much heat (in kilocalories) is needed to convert 1.00 kg of ice at 0°C into steam at 100°C?

A 5-kg piece of lead (specific heat 0.03 cal/g⋅°C) having a temperature of 80°C is added to 500 g of water having a temperature of 20°C. What is the final equilibrium temperature (in °C) of the system?

An 8000-kg aluminum flagpole 100 m long is heated by the Sun from a temperature of 10°C to 20°C. Find the work done (in J) by the aluminum if the linear expansion coefficient is 24 × 10⁻⁶ (°C) −1. (The density of aluminum is 2.7 × 10³ kg/m³ and 1 atm = 1.0 × 10⁵N/m².)

Five moles of an ideal gas expands isothermally at 100°C to five times its initial volume. Find the heat flow into the system.

If 25 kg of ice at 0°C is combined with 4 kg of steam at 100°C, what will be the final equilibrium temperature (in °C) of the system?

An 8000-kg aluminum flagpole 100-m long is heated by the Sun from a temperature of 10°C to 20°C. Find the heat transferred (in J) to the aluminum if the specific heat of aluminum is 0.215 cal/g⋅°C.

A slab of concrete and an insulating board are in thermal contact with each other. The temperatures of their outer surfaces are 68°F and 50°F. Determine the rate of heat transfer (in BTU/ft2⋅h) if the R values are 1.93 and 8.7 ft2⋅°F⋅h/BTU, respectively.

Quiz 21: Heat and the First Law of Thermodynamics

A 5-g coin is dropped from a 300-m building. If it reaches a terminal velocity of 45 m/s, and the rest of the energy is converted to heating the coin, what is the change in temperature (in °C) of the coin? (The specific heat of copper is 387 J/kg⋅°C.)

Determine the heat capacity (in calories/°C) of a lake containing one million gallons (approximately 4 million kilograms) of water at 15°C.

A 5-gallon container of water (approximately 20 kg) having a temperature of 212°F is added to a 50-gallon tub (approximately 200 kg) of water having a temperature of 50°F. What is the final equilibrium temperature (in °C) of the mixture?

How much heat (in kcal) must be removed to make ice at −10°C from 2 kg of water at 20°C? (The specific heat of ice is 0.50 cal/g⋅°C.)

A 300-g glass thermometer initially at 25°C is put into 200 cm3 of hot water at 95°C. Find the final temperature (in °C) of the thermometer, assuming no heat flows to the surroundings. (The specific heat of glass is 0.2 cal/g⋅°C.)

Which statement below regarding the first law of thermodynamics is most correct?

A child has a temperature of 101°F. If her total cross-sectional area is 2 m2, find the energy lost each second (in W) due to radiation, assuming the emissivity is 1. (Assume the room temperature is 70°F.)

How many calories of heat are required to raise the temperature of 4 kg of water from 50°F to the boiling point?

How much heat, in joules, is required to convert 1.00 kg of ice at 0°C into steam at 100°C? (LF,ice = 333 J/g; LV,steam = 2.26 × 103 J/g.)

In an adiabatic free expansion

One gram of water is heated from 0°C to 100°C at a constant pressure of 1 atm. Determine the approximate change in internal energy (in cal) of the water.

How much heat (in kilocalories) is needed to convert 1.00 kg of ice at 0°C into steam at 100°C?

A 5-kg piece of lead (specific heat 0.03 cal/g⋅°C) having a temperature of 80°C is added to 500 g of water having a temperature of 20°C. What is the final equilibrium temperature (in °C) of the system?

An 8000-kg aluminum flagpole 100 m long is heated by the Sun from a temperature of 10°C to 20°C. Find the work done (in J) by the aluminum if the linear expansion coefficient is 24 × 10−6 (°C) −1. (The density of aluminum is 2.7 × 103 kg/m3 and 1 atm = 1.0 × 105 N/m2.)

Five moles of an ideal gas expands isothermally at 100°C to five times its initial volume. Find the heat flow into the system.

If 25 kg of ice at 0°C is combined with 4 kg of steam at 100°C, what will be the final equilibrium temperature (in °C) of the system?

An 8000-kg aluminum flagpole 100-m long is heated by the Sun from a temperature of 10°C to 20°C. Find the heat transferred (in J) to the aluminum if the specific heat of aluminum is 0.215 cal/g⋅°C.

A slab of concrete and an insulating board are in thermal contact with each other. The temperatures of their outer surfaces are 68°F and 50°F. Determine the rate of heat transfer (in BTU/ft2⋅h) if the R values are 1.93 and 8.7 ft2⋅°F⋅h/BTU, respectively.

A 300-g glass thermometer initially at 25°C is put into 200 cm³ of hot water at 95°C. Find the final temperature (in °C) of the thermometer, assuming no heat flows to the surroundings. (The specific heat of glass is 0.2 cal/g⋅°C.)

A child has a temperature of 101°F. If her total cross-sectional area is 2 m², find the energy lost each second (in W) due to radiation, assuming the emissivity is 1. (Assume the room temperature is 70°F.)

How much heat, in joules, is required to convert 1.00 kg of ice at 0°C into steam at 100°C? (LF,ice = 333 J/g; LV,steam = 2.26 × 10³ J/g.)

An 8000-kg aluminum flagpole 100 m long is heated by the Sun from a temperature of 10°C to 20°C. Find the work done (in J) by the aluminum if the linear expansion coefficient is 24 × 10⁻⁶ (°C) −1. (The density of aluminum is 2.7 × 10³ kg/m³ and 1 atm = 1.0 × 10⁵N/m².)