A heating cool of nichrome wire with cross sectional area of 0.1mm^2 opeeate on a 12V supply and has a power of 36w when immersed in water at 373k calculate the length of wire?

To calculate the length of the wire, we can use the formula for power:

P = V^2 / R

Where:
P = power (36W)
V = voltage (12V)
R = resistance of the wire

We can rearrange the formula to solve for resistance:

R = V^2 / P
R = 12^2 / 36
R = 4 ohms

Now, we can calculate the resistance of the wire using the formula:

R = ρ * L / A

Where:
ρ = resistivity of nichrome wire (1.10 x 10^-6 ohm.m)
L = length of the wire
A = cross-sectional area of the wire (0.1mm^2 = 1 x 10^-7 m^2)

Substitute the values into the formula:

4 = (1.10 x 10^-6) * L / (1 x 10^-7)
4 = 11 * L
L = 4 / 11
L = 0.3636 meters

Therefore, the length of the nichrome wire is approximately 0.3636 meters.

Given:
Cross-sectional area of nichrome wire, A = 0.1 mm² = 10^-6 m²
Voltage, V = 12 V
Power, P = 36 W
Temperature of water, T = 373 K

To find:
Length of the wire, l

Using the relation for power in a resistor:

P = V²/R

where R is the resistance of the wire.

The resistance of the wire can be expressed as:

R = ρ - l / A

where ρ is the resistivity of nichrome, l is the length of the wire, and A is the cross-sectional area.

Substituting the expression for R into the power equation:

P = V² / (ρ - l / A)

Solving for l:

l = V² - A / (P - ρ)

Substituting the given values:

ρ for nichrome = 1.0 x 10^-6 Ωm
l = (12 V)² - (10^-6 m²) / (36 W - 1.0 x 10^-6 Ωm)
l = 3.6 m

Therefore, the length of the nichrome wire is 3.6 meters.