Concept of heat and work
Work
The product of force and displacement is known as work. i.e.,
Work = Force × Displacement
W = F × ℓ
Consider a gas enclosed in a cylinder fitted with a frictionless piston.
Suppose,
a = area of cross section of the cylinder.
p = pressure of the piston
V1 = Initial volume of the gas
V2 = final volume of the gas (by expansion)
ℓ = displacement of the piston
Work done by the gas (in expansion) is given by,
W = F × ℓ
As we know, p = F/a ⇒F = p × a
∴ W = p × a × ℓ
As we know, change in volume = V2-V1 = a × ℓ
⇒W = p × (V2-V1)
⇒W = p ΔV
In general, W = -pext ΔV ( acc. to chemistry)
If system works ⇒V2 > V1 ⇒ work = -ve
If work is done on the system⇒V2<V1⇒work= +ve
or
for compression, work done will be positive; and
for expansion, work done will be negative.
Heat
Heat may be defined as the quantity of energy which flows between a system and its surrounding on account of temperature difference.
Heat always flow from higher temperature to a lower temperature.
If heat is flowing into the system ⇒ q = +ve
If heat is flowing out of the system ⇒ q = -ve
Units of heat and work
Calorie, it is defined as the quantity of heat required to raise the temperature of 1gm of water by 1°C (14.5 to 15.5°C)
Since heat and work are interrelated.
1Nm = 1J = 10⁷ erg = 0.239 cal
1 cal = 4.184 J ≈ 4.2 J
1L-atm = 101.3 J = 24.206 cal = 101.3 × 10⁷ erg
1 L-atm > 1 Cal. > 1J > 1erg
Sign convention of heat (q) and work (W)
Heat flows into the system ⇒ q = + ve
Heat flows out of the system ⇒ q = – ve
Work is done on the system ⇒ W = + ve
Work is done by the system ⇒ W = – ve
- When heat flows into the system from the surrounding, the energy of system increases. Thus it is taken to be positive i.e., +q
- When heat flows from the system to the surrounding, the energy of system decreases. Thus it is taken to be negative i.e., -q
- If work is done on the system by the surrounding then the energy of system is increases. Thus it is taken to be positive i.e., +W
- If work is done by the system on the surrounding then the energy of system is decreased. Thus it is taken to be negative i.e., -W
Nature of Heat and Work
Whenever a system changes from one state to another, there is always a change in energy. This change in energy may appear in the form of heat, work and light etc.
Unit of energy is joule.
- 1 joule is the amount of work done when a body moves under a force of 1N in a distance of 1meter in the direction of force.
or it is defined as the work done when a resistance of 1N is moved through a distance of 1meter.
Thus J = N.m
i.e., 1 joule of work is done when a force of 1 Newton moves a distance of 1 meter. - In 1850, James P. Joule showed that, there is a definite relationship between mechanical work (W) and heat produced H .
(If we rub our palms together, we feel the warmth)
W ∝ H
⇒ W = JH
where, J = Joule mechanical equivalent of heat. Its numerical value is taken as 4.184 Joules.
Thus with expenditure of 4.184 joules of mechanical energy, 1 calorie of heat is produced.
i.e., 1 calorie = 4.184 joules
In SI system, the unit of energy is Joule.
In CGS system, the unit of energy is erg.
1 Joule = 10⁷ ergs
For large quantity of work done we often use kilo-joule (kJ). 1kJ = 1000 J
Other Important Points to be learn
Energy manifests itself in many forms, e.g., in form of mechanical work (as in case of Joule-Thomson experiment) , heat energy, chemical energy, mechanical energy etc.
Energy is composed of two factors in each of these forms. These two factors are :
1. an intensity factor
2. a capacity factor
The product of these two factors gives the energy.
For example-
- Heat is measured by the product of temperature ( intensity factor) and heat capacity ( capacity factor). Product of these two gives the energy of the system.
If a substance having mass m kg and specific heat s kJ per kg is heated through temp. t°C, then the heat involved is given by (mst) kJ. - When a current flows in an electric circuit for a given interval of time, then electrical energy is produced viz., obtained by the product of potential difference V ( intensity factor) causing the current to flow and the quantity of electricity Q ( capacity factor) that flows for that interval of time. Let V measured in volts and Q in coulombs.The product of these two factors express the electrical energy (or work) in volt-coulombs viz., joules
- When a body of mass m kg moved through a height of h meter, the work done against gravity is obtained by multiplying the intensity factor (mg newtons) and the capacity factor (h meters).Thus, the work performed is given by multiplying these two factors i.e., (mg×h) Joules. This work gets stored in the body as potential energy and is released when the body falls back to its original position.
