Unit: Thermodynamics
Chapter: Forces, Heat and energy transfer
Reference: AP Physics Algebra, Thermodynamics, Forces, Heat and energy transfer, The first law of thermodynamics, Conventions, Heat (Q), Internal Energy (E or U) Or Hidden Energy, Specific Heat Capacity, Modes of Heat Transfer
After studying this chapter, you should be able to know,
- The first law of thermodynamics
- The internal energy of the system
- Specific Heat Capacity
- Mode of heat transfer
The first law of thermodynamics
It states that the change in internal energy of a system during a thermodynamic process is equal to the sum of the heat given to it and the work done on it.
Suppose that ΔQ amount of heat is given to the system and – ΔW work is done on the system. Then increase in internal energy of the system, ΔU, according to the first law of thermodynamics is given by
ΔU = ΔQ – ΔW
This is the mathematical form of the first law of thermodynamics. Here ΔQ, ΔU and ΔW all are in SI units.
The first law of thermodynamics can also be written as
ΔQ = ΔU + ΔW
The signs of ΔQ, ΔU and ΔW are known from the following sign
conventions:
- Work done (ΔW) by a system is taken as positive whereas the work done on a system is taken as negative. The work is positive when a system expands.
- When a system is compressed, the volume decreases, and the work done is negative. The work done does not depend on the initial and final thermodynamic states; it depends on the path followed to bring a change.
- Heat gained by (added to) a system is taken as positive, whereas heat lost by a system is taken as negative.
- The increase in internal energy is taken as positive and a decrease in internal energy is taken as negative.
- If a system is taken from state 1 to state 2, it is found that both ΔQ and ΔW depend on the path of transformation. However, the difference (ΔQ – ΔW) which represents ΔU, remains the same for all paths of transformations. We, therefore, say that the change in internal energy ΔU of a system does not depend on the path of the thermodynamic transformations.
Limitations of the First Law of Thermodynamics
• You know that heat always flows from a hot body to a cold body. But the first law of thermodynamics does not prohibit the flow of heat from a cold body to a hot body. It means that this law fails to indicate the direction of heat flow.
• You know that when a bullet strikes a target, the kinetic energy of the bullet is converted into heat. This law does not indicate why heat developed in the target cannot be changed into the kinetic energy of a bullet to make it fly. It means that this law fails to provide the conditions under which heat can be changed into work. Moreover, it has obvious limitations in indicating the extent to which heat can be converted into work.
Heat (Q)
- By difference in temperature, the total amount of energy transferred from one body to another is known as Heat.
- Sign convention: Heat absorb by the system (+) Heat evolved by the system (–)
Internal Energy (E or U) Or Hidden Energy
1. Sum of various types of energy related to a system is known as internal energy E or U = P.E + K.E + T.E + ……
2. Energy due to gravitational pull is not considered in internal energy
3. It is impossible to calculate the absolute value of internal energy because it is not possible to calculate the exact value of all types of energy at a time
4. Internal energy is an extensive property
5. It is a state function
6. Relation between Internal Energy & Pressure for 1 mole of an ideal gas and per unit volume.
In ideal gas internal energy = KE
(1 mole)
PV = nRT
P × 1 = 1 × RT
P = RT
7. The properties which arise out of the collective behaviour of a large number of chemical entities. Example. Pressure, volume temperature, composition, colour refractive index etc.
Specific Heat Capacity
Suppose an amount of heat rQ supplied to a substance changes its temperature from T to T + rT. We define the heat capacity of a substance to be
s=∆Q∆T
We expect rQ and, therefore, heat capacity S to be proportional to the mass of the substance. Further, it could also depend on the temperature, i.e., a different amount of heat may be needed for a unit rise in temperature at different temperatures. To define a constant characteristic of the substance and independent of its amount, we divide S by the mass of the substance m in kg:
s=Sm=1m ∆Q∆T
s is known as the specific heat capacity of the substance. It depends on the nature of the substance and its temperature. The unit of specific heat capacity is J kg–1 K–1.
If the amount of substance is specified in terms of moles μ (instead of mass m in kg), we can define heat capacity per mole of the substance by
C=Sμ=1μ ∆Q∆T
C is known as the molar specific heat capacity of the substance. Like s, C is independent of the amount of substance. C depends on the nature of the substance, its temperature and the conditions under which heat is supplied. The unit of C is J mo1–1 K–1.
Modes of Heat Transfer
There are basically three modes:
1. Conduction
2. Convection and
3. Radiation.
Conduction
- Thermal conduction is the transfer of thermal energy from the high energy to the low energetic particles of a stationary medium (solids, liquids or gas) due to interactions between the particles.
- In solids, conduction may be attributed to atomic activity in the form of lattice vibrations and energy transport by the free electrons.
- In fluids, conduction occurs due to the collisions and diffusion of the molecules during their random motion. It is a microscopic form of heat transfer.
Convection
Convection refers to the thermal energy transfer between a solid surface and a moving fluid when they are at different temperature levels.
- It involves the combined effect of conduction and fluid motion.
- Heat is transferred from the solid surface to the fluid layer which is in contact with it by conduction.
- Then to the adjacent layers, heat will transfer by the random molecular motion.
Radiation
- Thermal energy transfer by radiation is caused by electromagnetic waves (or photons).
- Thermal radiation is emitted by all surfaces which are kept at a finite temperature level.
- This happens from solids, liquids and gases.
- Rate of emission increases with temp. level.
- Radiant energy does not require a material medium for its transport.
- Moreover, radiation transfer will occur effectively in a vacuum.
Example:
If ∆𝑄 and ∆𝑊 represent the heat supplied to the system and the work done on the system respectively, then the first law of thermodynamics can be written as Where ∆𝑈 is the internal energy _________
Solution:
From FLOT Δ𝑄 = Δ𝑈 + Δ𝑊
∵ Heat is supplied to the system so Δ𝑄 → Positive
and work is done on the system so Δ𝑊 → Negative
Hence, + Δ𝑄 = Δ𝑈 – Δ𝑊
Key points:
- Specific heat capacity is the quantity of heat needed to raise the temperature per unit mass.
- Usually, it's the heat in Joules needed to raise the temperature of 1 gram of sample 1 Kelvin or 1 degree Celsius.
- Water has an extremely high specific heat capacity, which makes it good for temperature regulation.
- Every equilibrium state of a thermodynamic system is completely described by specific values of some macroscopic variables, also called state variables.
- The specific heat capacity of a substance depends on its chemical composition, physical state (solid, liquid or gas), and temperature. Different substances have different specific heat capacities, which is why some materials feel warmer or colder to the touch even though they may be at the same temperature.
- The specific heat capacity can be calculated using the formula:
Q = mcΔT
- Where Q is the amount of heat energy absorbed or released by the substance, m is the mass of the substance, c is the specific heat capacity of the substance, and ΔT is the change in temperature of the substance.