Understanding the Unit of θ in the Equation ΔT = Pθ

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SUMMARY

The equation ΔT = Pθ defines the relationship between temperature difference (ΔT), power (P), and the unit θ. In this context, power is measured in Joules per second (W), and through dimensional analysis, θ is determined to have the unit of m² kg/s³. This conclusion aligns with the principles of thermodynamics, specifically the first law of thermodynamics, which relates energy transfer to temperature changes.

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Homework Statement


In the equation ΔT = Pθ, P is power in Joules per second and ΔT is the temperature difference in °C. Use dimensional analysis to find the unit of θ. Hint, Joules has units of Force time distance.

My question is: I don't understand what they mean by finding the unit of θ. Are they saying that P needs to be multiplied by θ, or does θ simply represent the unit of P that I have worked out below ?
Sorry, I am unfamiliar with how Physics questions are worded.

The Attempt at a Solution


I am pretty sure the answer is m^2 kg / s^3
If correct, how does my answer relate to θ ?
 
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This expression is the first law of thermo. See if you can find an equation for theta based on physical constants and variables and I think it will make sense.
 
thanks, so is my answer of m^2 kg / s^3 not correct ?
 

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