Question 1

If, with steady state heat flow established, you double the thickness of a wall built from solid uniform material, the rate of heat loss for a given temperature difference across the thickness will

Accepted Answer

The rate of heat loss is inversely proportional to the thickness of the wall. If the thickness is doubled, the rate of heat loss will become one-half its original value.

Question 2

On a cold day, a piece of metal feels much colder to the touch than a piece of wood. This is due to the difference in which one of the following physical properties of these materials?

Accepted Answer

Thermal conductivity is the property that explains why metal feels colder than wood. Metals typically have higher thermal conductivity than wood, meaning they can transfer heat away from your skin more quickly, making them feel colder.

Question 3

A person running in place on an exercise machine for 10 min uses up 17 kcal (food calories). Another person exercises by repeatedly lifting two 2.5-kg weights a distance of 50 cm. How many
Repetitions of this exercise are equivalent to 10 minutes of running in place? Assume that the
Person uses negligible energy in letting down the weights after each lift. (1 cal = 4.186 J)

Accepted Answer

To find the number of repetitions, first convert 17 kcal to joules: 17 kcal * 4186 J/kcal = 71162 J. The work done per lift is mgh = 2 * 2.5 kg * 9.8 m/s² * 0.5 m = 24.5 J. Divide the total energy by the energy per lift: 71162 J / 24.5 J/lift ≈ 2905 repetitions.

Question 4

An object having a fixed emissivity of 0.725 radiates heat at a rate of 10 W when it is at an absolute temperature T. If its temperature is doubled to 2T, at what rate will it now radiate?

Accepted Answer

The rate at which an object radiates heat is given by the Stefan-Boltzmann law, which states that the power radiated per unit area of a black body is proportional to the fourth power of the absolute temperature (P ∝ T^4). When the temperature is doubled (T becomes 2T), the power radiated increases by a factor of (2^4) = 16. Therefore, if the object originally radiates at 10 W, when the temperature is doubled, it will radiate at 10 W * 16 = 160 W.

Question 5

A heat pump absorbs heat from the atmosphere at a rate of 30 kW. If work is being done to run this heat pump at a rate of 7.7 kW, what is the coefficient of performance (COP) of the heat pump?

Accepted Answer

The coefficient of performance (COP) of a heat pump is defined as the ratio of the heat output to the work input. In this case, COP = Heat absorbed / Work done = 30 kW / 7.7 kW = 3.896 or approximately 4.9.

Question 6

A solid cylindrical bar conducts heat at a rate of 25 W from a hot to a cold reservoir under steady state conditions. If both the length and the diameter of this bar are doubled, the rate at which it
Will conduct heat between these reservoirs will be

Accepted Answer

The rate of heat conduction ($Q$) through a cylindrical bar is given by Fourier's law of heat conduction, $Q = \frac{kA(T_{hot} - T_{cold})}{L}$, where $k$ is the thermal conductivity, $A$ is the cross-sectional area, $T_{hot}$ and $T_{cold}$ are the temperatures of the hot and cold reservoirs, respectively, and $L$ is the length of the bar. Doubling both the diameter and the length of the bar quadruples the cross-sectional area ($A$) but also doubles the length ($L$). These changes result in the heat conduction rate being doubled ($2 \times 25 W = 50 W$).

Question 7

A person consumes a snack containing 14 food calories (14 kcal). What is the power this food produces if it is to be "burned off" due to exercise in 6 hours? (1 cal = 4.186 J)

Accepted Answer

First, convert food calories to joules: 14 kcal * 1000 cal/kcal * 4.186 J/cal = 58504 J. Then, divide by time in seconds (6 hours * 3600 seconds/hour) to find power in watts: 58504 J / 21600 s = 2.7 W.

Question 8

A 4.0-kg aluminum block is originally at 10°C. If 160 kJ of heat is added to the block, what is its final temperature? The specific heat capacity of aluminum is 910 J/kg · K.

Accepted Answer

To find the final temperature, use the formula: Q = mcΔT, where Q is the heat added (160,000 J), m is the mass (4.0 kg), c is the specific heat capacity (910 J/kg·K), and ΔT is the change in temperature. Solving for ΔT gives ΔT = Q / (mc) = 160,000 / (4.0 * 910) = 44°C. The initial temperature is 10°C, so the final temperature is 10°C + 44°C = 54°C.

Question 9

A heat pump with a performance coefficient (COP) of 4.9 absorbs heat from the atmosphere at a rate of 29 kW. At what rate is work being done to run this heat pump?

Accepted Answer

The work done to run the heat pump can be calculated using the formula: Work = Q / COP, where Q is the heat absorbed from the atmosphere (29 kW) and COP is the coefficient of performance (4.9). Thus, Work = 29 kW / 4.9 = 5.918 kW, which rounds to approximately 6 kW.

Question 10

Two metal spheres are made of the same material and have the same diameter, but one is solid and the other is hollow. If their temperature is increased by the same amount,

Accepted Answer

When both spheres are made of the same material and have the same diameter, and their temperature is increased by the same amount, both will expand equally due to thermal expansion. The fact that one is solid and the other is hollow does not affect the amount by which their outer dimensions increase, as expansion depends on the material's properties and the temperature change, not on the object's mass or whether it is solid or hollow.

Question 11

A thermally isolated system is made up of a hot piece of aluminum and a cold piece of copper, with the aluminum and the copper in thermal contact. The specific heat capacity of aluminum is
More than double that of copper. Which object experiences the greater magnitude gain or loss of
Heat during the time the system takes to reach thermal equilibrium?

Accepted Answer

In a thermally isolated system, the heat lost by one object is equal to the heat gained by the other, ensuring energy conservation. Thus, both objects experience the same magnitude of heat change.

Question 12

How much heat is required to raise the temperature of a 225-g lead ball from 15.0°C to 25.0°C? The specific heat of lead is 128 J/kg · K.

Accepted Answer

The answer of How much heat is required to raise...

Question 13

An ideal Carnot engine is operated as a heat pump to heat a room in the winter. The heat pump delivers heat to the room at the rate of 47 kJ per second and maintains the room at a temperature
Of 293 K when the outside temperature is 237 K. The power requirement to run the heat pump
Under these operating conditions is closest to

Accepted Answer

The efficiency of a Carnot heat pump is given by the formula: $$COP = \frac{T_{hot}}{T_{hot} - T_{cold}}$$, where $T_{hot}$ and $T_{cold}$ are the temperatures of the hot and cold reservoirs, respectively, in Kelvin. Here, $T_{hot} = 293K$ and $T_{cold} = 237K$. Thus, $$COP = \frac{293}{293 - 237} = \frac{293}{56}$$.The power requirement $P$ can be calculated using the formula: $$P = \frac{Q}{COP}$$, where $Q$ is the heat delivered per second (47 kJ/s or 47000 W). Substituting the values, we get: $$P = \frac{47000}{\frac{293}{56}} = \frac{47000 \times 56}{293}$$.Calculating this gives $P \approx 9000 W$, which is closest to option E.

Question 14

If the absolute temperature of an object is tripled, the thermal power radiated by this object (assuming that its emissivity and size are not affected by the temperature change) will

Accepted Answer

According to the Stefan-Boltzmann law, the thermal power radiated by an object is proportional to the fourth power of its absolute temperature (P ∝ T^4). If the temperature is tripled, the power increases by a factor of 3^4 = 81.

Question 15

Which one of the following quantities is the smallest unit of heat energy?

Accepted Answer

The joule is the smallest unit of heat energy listed, as it is the standard unit of energy in the International System of Units (SI). A calorie is larger than a joule, a kilocalorie is 1,000 calories, and a British Thermal Unit (Btu) is also larger than a joule.

Question 16

If you wanted to know how much the temperature of a particular piece of material would rise when a known amount of heat was added to it, which of the following quantities would be most
Helpful to know?

Accepted Answer

The specific heat of a material is the amount of heat per unit mass required to raise the temperature by one degree Celsius. Knowing the specific heat is essential for calculating the temperature change when a known amount of heat is added to a material.

Question 17

By what primary heat transfer mechanism does the sun warm the earth?

Accepted Answer

The primary mechanism by which the sun warms the Earth is radiation. Heat is transferred through the vacuum of space from the sun to the Earth without the need for a medium, which is characteristic of radiation. Conduction and convection require material media for heat transfer and are not significant in the vacuum of space between the sun and Earth.

Question 18

At room temperature, a typical person loses energy to the surroundings at the rate of 62 W. If this energy loss has to be made up by an equivalent food intake, how many kilocalories (food calories)
Does this person need to consume every day just to make up this heat loss? (1 cal = 4.186 J)

Accepted Answer

First, convert the energy loss rate from watts to joules per day: $62 \, \text{W} = 62 \, \text{J/s}$. There are $86400 \, \text{s}$ in a day, so the daily energy loss is $62 \, \text{J/s} \times 86400 \, \text{s/day} = 5356800 \, \text{J/day}$. To convert joules to calories, divide by $4.186 \, \text{J/cal}$: $5356800 \, \text{J} / 4.186 \, \text{J/cal} = 1280400 \, \text{cal}$. Since $1 \, \text{kcal} = 1000 \, \text{cal}$, the daily energy loss in kcal is $1280400 \, \text{cal} / 1000 = 1280 \, \text{kcal}$. The closest answer is 1300 kcal.

Question 19

The process in which heat flows by the mass movement of molecules from one place to another is known as

Accepted Answer

Convection is the process of heat transfer through the movement of mass from one place to another, typically in fluids (liquids or gases) where warmer parts of the fluid rise and cooler parts sink, setting up a circulation that transfers heat.

Question 20

A thermally isolated system is made up of a hot piece of aluminum and a cold piece of copper, with the aluminum and the copper in thermal contact. The specific heat capacity of aluminum is
More than double that of copper. Which object experiences the greater temperature change during
The time the system takes to reach thermal equilibrium?

Accepted Answer

The answer of A thermally isolated system is made up...

Quiz 2: Describing Motion: Kinematics in One Dimension