What is the unit of the rate of heat transfer (P) and what is the unit of thermal conductivity (k)?

Question

BlackTom AI · Accepted Answer

We start by identifying the physical quantities and their standard units.
- The rate of heat transfer P is power, which is energy per unit time. In the SI system, energy (joule) divided by time (second) gives the unit watt (W). Therefore P should be expressed in W.
- Thermal conductivity k relates heat transfer to the temperature gradient in a material. Its SI unit is watts per meter per degree Celsius (or per kelvin, since temperature difference is involved). This is written as W/(m·°C) or W/m·K. Thus k should be expressed in W/m·°C.
Now let's evaluate each option:

Option a: P is in W/m, k is in W/s·°C.
- P in W/m would imply a power per unit length, which is not the standard unit for total rate of heat transfer. The rate of heat transfer P is not inherently per meter of something; it is a total power, so W/m is inappropriate. 
- k in W/s·°C is also incorrect because thermal conductivity is not a rate with respect to time; it is a material property that scales with distance, hence units involve per meter and per degree Celsius, not per second.

Option b: P is in J, k is in J/m·°C.
- P in joules would be energy, not a rate. The question asks for the unit of the rate of heat transfer, which must be a power unit (J/s or W). So J is incorrect. 
- k in J/m·°C is wrong because thermal conductivity is not energy per length per temperature difference; it is a material property with units W/(m·°C), so J/m·°C is not standard for k.

Option c: P is in W, k is in W/m·°C.
- P in W correctly represents power (heat transfer rate). This aligns with the definition of P as the rate of heat transfer.
- k in W/m·°C is the standard unit for thermal conductivity, expressing how much heat per unit length per unit temperature difference passes through a material. This matches the conventional SI unit.

Option d: P is in W/s, k is in J/s·°C.
- P in W/s would be a rate of change of power, which is not a standard quantity for heat transfer rate. W/s would imply how power changes with time, not the instantaneous rate itself. This is inappropriate here.
- k in J/s·°C would mix energy flow rate with time per temperature, which is not the accepted unit for thermal conductivity. The correct form should be W/(m·°C), not J/s·°C.

In summary, each incorrect option either mislabels P as a non-rate quantity (J) or misstates the units for k, or combines both inappropriately. The standard, scientifically accepted pair of units for the rate of heat transfer and for thermal conductivity is P in W and k in W/m·°C, respectively.

What is the unit of the rate of heat transfer (P) and what is the unit of thermal conductivity (k)?单项选择题

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