Download Heat is energy transferring in a system and its surroundings.

Heat
Heat is energy transferring in a system and its surroundings.
Closed vs. open systems
A closed system is one for which no mass enters or leaves
(but energy may be exchanged with the environment).
An open system is one for which mass may enter or leave
(as may energy).
Heat is
(a) a fluid called caloric.
(b) a measure of the average kinetic energy of atoms.
(c) the amount of energy transferred between objects as a
result of a difference in temperature.
(d) an invisible, odorless, weightless substance.
(e) the total kinetic energy of an ideal gas.
Internal energy
Internal energy (or “thermal energy”) is the sum
total of all of the energy of all of the molecules in a
system.
Internal energy of nobel (monatomic) ideal gases
•
•
•
•
•
There is no orientational order.
There are no chemical bonds.
There is no vibrational kinetic energy.
There is no aggregation.
Only kinetic energy.
Internal energy of nobel ideal gases (cont.)
The kinetic energy of a monotonic ideal gas is simply
From thermodynamics, we know
Therefore,
Specific heat
The amount of heat, , required to change the temperature of
a given material is proportional to the mass, , of the material
present and to the change in temperature,
.
The constant, , is called the specific heat.
How much heat input is needed
to raise the temperature of an
empty 10 kg vat made of copper
from 10°C to 60°C?
What if the vat is also filled with
20 kg of water?
A 1.50 kg sample of the alloy is heated to 540°C. It is then
quickly placed in 4.00 kg of water at 10.0°C, which is
contained in a large 2.00 kg aluminum calorimeter bowl.
The final temperature of the system is 30.5°C.
Determine the specific heat of the alloy.
Two objects are made of the same material, but they have
different masses and temperatures. If the objects are brought
into thermal contact, which one will have the greater
temperature change?
(a) The one with the higher initial temperature.
(b) The one with the lower initial temperature.
(c) The one with the greater mass.
(d) The one with the lesser mass.
(e) The one with the higher specific heat.
(f) Not enough information.
Two equal-mass liquids, initially at the same temperature,
are heated for the same time over the same stove. You
measure the temperatures and find that one liquid has a
higher temperature than the other. Which liquid has the
higher specific heat?
(a) The cooler one.
(b) The hotter one.
(c) Both are the same.
Specific heat for gases
The specific heat for gases is trickier because the volume
and pressure can change with a change in temperature
(remember
).
We define two types of specific heats; is the specific heat at
constant pressure, and is the specific heat at constant volume.
How much heat does it take to increase the temperature of
2.0 kg of steam from 150 oC to 170 oC when held at constant
volume?
How much heat for constant pressure?
Latent heat
The latent heat is the energy involved in the change of phase
for a material.
The heat required to change a material from the liquid to solid
state (or solid to liquid state) is called the heat of fusion.
The heat required to change a material from the liquid to gas
state (or gas to liquid state) is called the heat of vaporization.
The heat involved in a change of phase also depends on
the total mass of the material.
Which of the following happens when a material undergoes
a phase change?
(a) The temperature changes.
(b) The chemical composition changes.
(c) Heat flows into or out of the material.
(d) The molecules break apart into atoms.
A 64-kg ice-skater moving at 7.50 m/s glides to a stop.
Assuming the ice is at 0°C and that 50% of the heat
generated by friction is absorbed by the ice, how much ice
melts?
Heat of fusion of water = 333 kJ/kg
What mass of steam at 100°C must be added to 1.00 kg of ice at
0°C to yield liquid water at 30°C?
Specific heat capacity of water = 4186 J/(kg oC), heat of fusion
of water = 333 kJ/kg, heat of vaporization of water = 2260 kJ/kg
A cube of ice is taken from the freezer at 0oC and placed in
an 85 g aluminum calorimeter filled with 310 g of water at
room temperature of 20.0°C. The final situation is all water
at 17.0°C. What was the mass of the ice cube?
Specific heat capacity of water = 4186 J/(kg oC), heat of
fusion of water = 333 kJ/kg, specific heat capacity of
aluminum = 900 J/(kg oC)
Rate of heating/cooling
Heat is transferred from one place or object to another in
three different ways:
• Conduction
• Convection
• Radiation
Heat is the flow of energy and the three different transfer mechanisms
relocate heat over a period of time (rate of heat transfer)
The rate at which heat flows is measured using dimensions of power.
Conduction
The heat flow, Q, over a time interval, t, is given by the relation
Convection
Convection is the transfer of heat from one place to another
by the motion of mass in a fluid.
Airflow at a beach is an example of natural convection, as is
the mixing that occurs as surface water in a body of water
cools and sinks.
Radiative heat transfer
The rate of heat radiation from an object is given by the
Stefan-Boltzmann law.
The emissivity is given by e which varies from 0 to 1.
(Dark objects have a high emissivity while light objects have a low emissivity)
The “A” in the above equation is the area of the emitter.
The Stefan-Boltzmann constant is s = 5.67×10-8 W∙m2∙K4.
Radiative transfer in an environment
Any object not only emits energy by radiation but also
absorbs energy radiated by other objects.
If an object of emissivity and area A is at a temperature
T2 it radiates energy at a rate
. If the object is
surrounded by an environment at temperature T1, the rate
at which the surroundings radiate energy is proportional
to
.
The net rate of radiant heat flow is
Radiation is emitted
(a) only by glowing objects such as the Sun.
(b) only by objects whose temperature is greater than the
temperature of the surroundings.
(c) only by objects with more caloric than their surroundings.
(d) by any object not at 0 K.
(e) only by objects that have a large specific heat.
A pot of hot water (e= 0.7) has an exposed area of approximately
0.05 m2 and holds 0.7 kg of tea at 95 oC and sits in a room at 20 oC.
[Stefan-Boltzmann is 5.67×10-8 W∙m-2∙K-4]
What is the rate of heat loss from the pot due to radiation?
What is the approximate temperature of the tea after 15 minutes.
[Specific heat of water is 4.186 kJ∙kg-1∙ oC-1]
Energy and Power
After a long hot shower, there is no hot water left in the 250 L
water heater (1 L = 0.001 m3). This suggests that the tank has
emptied and refilled with water at roughly 14 oC.
How much energy does it take to reheat the water to 47 oC?
[specific heat capacity of water to be 4.186 kJ∙kg-1∙ oC-1]
How much time does it take to raise the water temperature
from 14 oC to 47 oC if the heater output is 9600 W?
How long does it take the Sun to melt a block of ice at 0°C
with a flat horizontal area 1.0 m2 and thickness 1.0 cm?
Assume that the Sun’s rays make an angle of 35° with the
vertical and that the emissivity of ice is 0.050.
[Use the heat of fusion of water = 333 kJ/kg and the
intensity of the sun = 1000 W/m2]
Laws of thermodynamics
First law of thermodynamics
The change in internal energy of a closed system, will be equal
to the energy added to the system by heating minus the work
done by the system on the surroundings.
Thermodynamic processes
Isothermal processes: Temperature does not change
in the system.
(
and therefore
)
Adiabatic processes: Heat does not flow in or out of
the system.
(Because
, the first law of thermodynamics gives
Isobaric processes: Pressure does not change in the
system.
Isovolumetric processes: Volume does not change in
the system.
)
An ideal gas undergoes an isothermal process. Which
of the following statements are true?
(i) No heat is added to or removed from the gas.
(ii) The internal energy of the gas does not change.
(iii) The average kinetic energy of the molecules does not
change.
(a) (i) only.
(b) (i) and (ii) only.
(c) (i) and (iii) only.
(d) (ii) and (iii) only.
(e) (i), (ii), and (iii).
Work done by volume changes in a gas
We originally learned that work is the force times the distance
and the cosine of the angle between them,
.
Pressure is the force per unit area, where work is also done by
a gas when there is a volume change (distance cubed) caused
from the gas under pressure. For an isobaric process, the
pressure is constant and
.
Second law of thermodynamics
Heat can flow spontaneously from a hot object to a cold
object, but heat will not flow spontaneously from a cold
object to a hot object.
Heat engines
Mechanical energy can be obtained from thermal energy
when heat is allowed to flow from a high temperature to a
low temperature.
Engines typically run in cycles. The starting point becomes
the end point for each cycle. Therefore,
per period.
The work of a heat engine is equal to the change in the heat
at the high temperature,
, and low temperature,
.
The efficiency, , of any heat engine can be defined as the ratio
of the work it does to the heat input at the high temperature.
OR
Entropy
Entropy is the measure of disorder in a system.
In thermodynamics, the change in entropy may be defined
by the heat added to the system in a reversible process at
constant temperature divided by the temperature.
For any thermodynamic process in a closed system, the
change in entropy is always greater than or equal to zero.
Unavailability of energy for work
In any process, no energy is ever lost (it is always conserved).
…but energy becomes less useful.
The amount of energy that becomes unavailable to do work is
proportional to the change in entropy during any process.
On a very hot day, could you cool your kitchen
by leaving the refrigerator door open?
(a) Yes, but it would be very expensive.
(b) Yes, but only if the humidity is below 50%.
(c) No, the refrigerator would exhaust the same amount
of heat into the room as it takes out of the room.
(d) No, the heat exhausted by the refrigerator into the
room is more than the heat the refrigerator takes out
of the room.
Which statement is true regarding the entropy
change of an ice cube that melts?
(a) Since melting occurs at the melting point temperature,
there is no temperature change so there is no entropy
change.
(b) Entropy increases.
(c) Entropy decreases.