Heat and power

Joule’s law:

Joule’s law state that,” the amount of heat generated in the conductor when the current is passed.”  it is denoted by H.

a. When different amount of current ( i ) is passed through the conductor heat is directly proportional to the square of the applied current for a constant time and resistance. i.e. H α i2……………….( i )

b. Heat generated in conductor is directly proprotional on the varying resistance ( R ) constant time and current. i.e H α R…………ii

c. Heat generated in a conductor is directly proportional on the varying time    ( t) for constant resistance and current. I.e. H α t……iii

Now from above equation ( i ), (ii ), and (iii ) we have a relation

H α i2 R t, therefore H= i2RtJ$\frac{{\mathrm{i}}^2\mathrm{R}\mathrm{t}}{\mathrm{J}}$ where J is joule’s mechanical equivalent of heat. Whose value is equal to 4.2 Jcal-1 Let us consider the e.m.f. of the cell is E is connected with the external resistance R and the current passing due E of the cell through that external resistance.

Then the potential drop ( V) in the external resistance occur and given by V = I R……i

Since i is the current passing through the external resistance R, then for the certain time t , the no. of the charge (q ) passes through the resistance is given by q = it………….ii.

Work done by the cell = W= Vq

Then from equation I, and ii,

We have W= i2R t ………………..iii

Since we have H = i2RtJ$\frac{{\mathrm{i}}^2\mathrm{R}\mathrm{t}}{\mathrm{J}}$ then H = WJ$\frac{\mathrm{W}}{\mathrm{J}}$

Therefore H= i2RtJ$\frac{{\mathrm{i}}^2\mathrm{R}\mathrm{t}}{\mathrm{J}}$ hence heat developed in the wire by passing the current is joule’s law was deduce.

Experimental verification of joule’s law:

Let us consider a calorimeter containing 2/3 rd water of calorimeter. A thermometer in insert into the water, a resistance coil is immersed into water of calorimeter and two end of coil are connected to terminal at the top of the box of calorimeter. A battery (B), an ammeter (A), a key (K) and rheostat are connected in series.

Verification of first law:

let us consider m and s be the mass and specific heat capacity of calorimeter and, M and S is the mass and specific heat capacity of water put in calorimeter. When the key is closed and constant current i1 recorded for the ammeter is passed and for a recorded time in travel t sec and raise in temperature in calorimeter is noted. Let ɵ1be the raise in temperature.

When the current is change i2  is passes for some in travel of time t sec and the temperature rise is ɵ2 and same process is repeated for different current

Now, heat produce in two experiment are H1and H2 and given by

H1=( ms +MS)ɵ1 ……………….1   

H2 =( ms +MS)ɵ2      …………….2

On dividing equation 1 by be we get

H1H2$\frac{{\mathrm{H}}_1}{{\mathrm{H}}_2}$=θ1θ2$\frac{{\theta }_1}{{\theta }_2}$……………3

From the recorded value it was found that

θ1θ2=i21i22$\frac{{\theta }_1}{{\theta }_2}=\frac{{\mathrm{i}}_1^2}{{\mathrm{i}}_2^2}$………….4

Now from 3 and 4 we have

i21i22=H1H2$\frac{{\mathrm{i}}_1^2}{{\mathrm{i}}_2^2}=\frac{{\mathrm{H}}_1}{{\mathrm{H}}_2}$or H α i2. This expression verify the first law of joule’s

Second law of joule’s

A constant current is pass for the same time in travel t sec through the different resistance by immersing in the water of calorimeter one by one and in each case the temperature was recorded let R1 and R2 be the resistance used and, ɵ1and ɵ2 be the rise in temperature across the resistance R1and R2 respectively. Also H1 and H2 be the heat generated in each cases and given by

 H1=(ms +MS)ɵ1……………….1   

H2 =(ms +MS)ɵ2…………….2

On dividing equation 1 by be we get

H1H2$\frac{{\mathrm{H}}_1}{{\mathrm{H}}_2}$=θ1θ2$\frac{{\theta }_1}{{\theta }_2}$……………3

From the recorded value it was found that

θ1θ2=R1R2$\frac{{\theta }_1}{{\theta }_2}=\frac{{\mathrm{R}}_1}{{\mathrm{R}}_2}$………….4

Now from 3 and 4 we have

R1R2=H1H2$\frac{{\mathrm{R}}_1}{{\mathrm{R}}_2}=\frac{{\mathrm{H}}_1}{{\mathrm{H}}_2}$  or H α R. This expression verifies the second law of joules.

Third law of joule’s

When a constant current is passed through the coil for for different time in travel say t1and t2  then the temperature rise is are ɵ1 and ɵ2 are recorded. Let heat generated in each process are H1and H2 and given by

H1=( ms +MS)ɵ1 ……………….1   

H2 =( ms +MS)ɵ2      …………….2

On dividing equation 1 by be we get

H1H2$\frac{{\mathrm{H}}_1}{{\mathrm{H}}_2}$=θ1θ2$\frac{{\theta }_1}{{\theta }_2}$……………3

From the recorded value it was found that

t1t2=H1H2$\frac{{\mathrm{t}}_1}{{\mathrm{t}}_2}=\frac{{\mathrm{H}}_1}{{\mathrm{H}}_2}$………….4

Or, H α t, as ɵα H, This expression verifies the third law of joules.

The element of heater is very hot but the wire carrying current is cold:

From his experiment, joule found that the amount of heat (H) produced in a conductor of resistance (R) due to the flow of current U for time t second is:

H = I2Rt.                                                                  

Or, H ∝  R for constant current (I) ad time (t):

Since, the element of the heater has very high resistance as compared to the current carrying wire. Hence, large amount of heat is produced in the heater but no in the wire, even though both of them carry the same current. Due to this reason the element of heater is very hot but the wire carrying current is cold.

Electric power: It is defined as the rate at which the work is done to maintain the steady current in an electrical circuit. Electrical power of an electrical energy is converted into other forms of energy. Its unit is watt.

Electrical energy: It is defined as the total work done to maintain the current in an electrical circuit for a given time.

Electrical energy = W = Vit = Pt.

Electrical energy = Electrical power * time.

SI – units of electrical energy is joule J.

In practice, electric energy is measured in Kilowatt hour.

EMF:

It is the property f a cell which moves all the charges in a fixed direction.

Terminal potential (V):

It is defined as the amount of work done by moving a unit charge from one electron to another when a load resistor is connected at the ends of cell.

Internal resistances(r):

The property electrolyte which restricts the flow of electric current through it across the ends of electrodes of cell is called internal resistance.

Relation between E,V and r for charging and discharging. When a cell of EMF E and internal resistance r is sending current (I) in a circuit, then the current flows in the cell in the direction of its EMF, This is called discharging of the cell. In this case, we have E = Ir + V, where V is the terminal p.d.

So, V = E – Ir

However, during the charging of a cell, a current is passed through the cell by an external source (S). The current sent by the source into the cell is along. A to B while the direction of emf of the cell is from B to A. Hence, the current (I) is flowing in the cell in opposite to its EMF. In this case, E = Vab – Ir, where Vab in terminal p.d.

So, Vab = E + Ir.

Hence, in this case the terminal p.d. across the cell is greater than its EMF. In other words, the terminal p.d. across a cell can be greater than its ENF during the charging of a cell.

Different between e.m.f.andp.d:

e.m.f.	p.d
The property of the cell that make the charge to move in a particular direction is e.m.f.	The potential difference between the positive and negative electrode of the cell when the current pass through external circuit.
It is reversible	It is irreversible.
It is always greater than p.d in closed circuit.	It is always less than emf in closed circuit.
It doesn’t depend upon the external resistance.	It is depends upon the external resistance.

The special characteristics of fused wire are:-

a) Rated current

b) Speed

c) The i2t value

d) Breaking Capacity

The special characteristics of heating wire is "Heating wire is used in the toaster, electric baseboard heater, blow-drier, percolator,
electric space heater, and in just about any other place where electricity is used to
produce heat. It's simply a. wire with more resistance than 'hook-up wire’.