The SI unit of thermal conductivity (K) is watt per metre per kelvin, written as W m^-1 K^-1. It can also be written as J s^-1 m^-1 K^-1, since 1 watt equals 1 joule per second. Memory hook: a bigger K means heat moves faster, so its unit carries "watt" (power, how fast) on top and "metre times kelvin" on the bottom.
Heat flows through a rod at rate H (in watts). Rearranging H = K A dT / L for K gives units of (W times m) / (m^2 times K) = W m^-1 K^-1, the SI unit of thermal conductivity.
Your doubts, answered
Is the unit W m^-1 K^-1 or J m^-1 K^-1?
Both describe the same thing, but W m^-1 K^-1 is the standard SI form. Thermal conductivity relates to the RATE of heat flow (heat per second = power), so the unit uses watt (W), not joule (J). If you use joule, you must include time: J s^-1 m^-1 K^-1. Since 1 W = 1 J s^-1, the two are identical. Plain J m^-1 K^-1 (with no seconds) is WRONG because it forgets time.
Why does watt appear on top of the unit?
Start from H = K A (delta T)/L, where H is the rate of heat flow. H is heat energy per second, so its unit is joule per second = watt. When you rearrange for K, watt stays in the numerator. So the unit naturally becomes watt divided by (metre and kelvin): W m^-1 K^-1.
What is the dimensional formula of thermal conductivity?
K = H L / (A delta T). Dimensions: H (power) = [M L^2 T^-3], L = [L], A = [L^2], delta T = [K]. So K = [M L^2 T^-3][L] / ([L^2][K]) = [M L T^-3 K^-1]. This matches the NCERT summary value [M L T^-3 K^-1].
How is W m^-1 K^-1 different from W m^-2 K^-1?
They belong to different quantities. W m^-1 K^-1 is thermal conductivity K (used in conduction through a rod, formula H = KA delta T / L). W m^-2 K^-1 is a heat transfer coefficient (used in convection/cooling, where per unit AREA matters). Do not mix them up: conductivity has metre to the power minus one, not minus two.
Does the length L in the formula affect the unit of K?
No. K is a material property, not a shape property. In H = KA delta T / L the length and area cancel out in a way that leaves K with the fixed unit W m^-1 K^-1 for any rod. Two rods of the same material have the same K even if their lengths differ.
⚠️ The NEET trap ✗ Picking J m^-1 K^-1 because thermal conductivity 'is about heat energy (joule)'. ✓ The correct SI unit is W m^-1 K^-1 (or J s^-1 m^-1 K^-1). Thermal conductivity is tied to the RATE of heat flow, so time (per second) must appear. J m^-1 K^-1 without seconds is dimensionally wrong. 🧠 Whenever a quantity uses joule, ask: is it energy or rate of energy? Conduction is a rate, so use watt, not bare joule.
Real NEET questions
NEET 2019
The SI unit of thermal conductivity is:
A · J m K^-1
B · J m^-1 K^-1
C · W m K^-1
D · W m^-1 K^-1 ✓
Solution: Step 1: Use the conduction formula H = K A (delta T) / L, where H is the rate of heat flow. Step 2: Rearrange for K: K = H L / (A delta T). Step 3: Put in units. H is power = watt (W). L = metre (m). A = square metre (m^2). delta T = kelvin (K). Step 4: K = (W times m) / (m^2 times K) = W m^-1 K^-1. So the correct option is D.
Solved Thermal Properties Of Matter NEET PYQs
Try the real previous-year questions from this chapter — each with the answer and a full solution.
Watt per metre per kelvin, written W m^-1 K^-1. An equivalent form is J s^-1 m^-1 K^-1 because 1 watt equals 1 joule per second.
What is the CGS unit of thermal conductivity?
In the CGS system it is cal s^-1 cm^-1 (degree C)^-1, that is calorie per second per centimetre per degree Celsius. For NEET, the SI unit W m^-1 K^-1 is what you must remember.
What does a high value of thermal conductivity mean?
A high K means the material conducts heat quickly, so metals like copper and silver have large K. A low K means the material is a good insulator, like wood or air.
Is the dimensional formula of thermal conductivity M L T^-3 K^-1?
Yes. K = H L / (A delta T) gives [M L^2 T^-3][L] / ([L^2][K]) = [M L T^-3 K^-1], as listed in the NCERT chapter summary.
Why can we also write the unit as J s^-1 m^-1 K^-1?
Because 1 watt = 1 joule per second. Replacing W with J s^-1 in W m^-1 K^-1 gives J s^-1 m^-1 K^-1. Both forms are correct and identical.
