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My practice problem reads “if the temperature of the atmosphere decreased by 1K everywhere, and the heat released is given to the top 100 meters of the ocean, the temperature of the ocean rises by $\delta T$ everywhere. Find $\delta T$ (Take specific heat capacity of the water to be $4.2kJK^{-1}kg^{-1}$. The mass of the atmosphere is $p_0/g$ where $p_0$ is surface pressure).”

Now my approach was first to calculate the enthalpy of the atmosphere, but I am unsure of how to do this with the mass. I know that $Q = mc\delta T$, but I would need to find $c$ for the atmosphere which I do not have.

From there, I think I would have to do $-(mc\delta T)_{air} = (mc\delta T)_{water}$, but I don’t know what $m_{water}$ would be.

What am I missing? Also, has my reasoning for how to solve the problem been correct? Thanks!

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    $\begingroup$ Change your title. You don't "absorb" temperature. You really mean if it reduces the temperature of the atmosphere by 1K. $\endgroup$
    – Bob D
    Nov 26 at 0:57
  • $\begingroup$ You know the pressure of the atmosphere at sea level. This is directly related to the weight of the column of air (approximately 1 kg per cm^2). You also know that for a diatomic gas (most of atmosphere) the heat capacity per mile is about 5/2 R. That should be enough of a hint, I hope. $\endgroup$
    – Floris
    Nov 26 at 3:21
  • $\begingroup$ $m_{ocean} = 250 \space m_{atmosphere}$. See What is the mass of our planet's atmosphere, hydrosphere, and cryosphere combined? $\endgroup$
    – mmesser314
    Nov 26 at 5:47