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I have huge vessel filled with $CH_4$ and another vessel filled with hydrogen. Lets assume they have the same mass of gas say $10kg$.

Now I heat both of them up to $500K$. Since the heat capacity of hydrogen is greater than that of $CH_4$ (for $H_2$ it is $14 KJ/kg-K$ and for $CH_4$ it is $2.889KJ/kg-k$), the amount of heat absorbed to raise the temperature of hydrogen is greater than $CH_4$ This is because $Q=mC_P\Delta T$ and m and $\Delta T$ are same for both $H_2$ and $CH_4$, $C_P$ is higher for hydrogen. Is this statement correct?

Now I let them cool to ambient. Assuming the heat transfer coefficients are same, the $CH_4$ would cool faster compared to the hydrogen vessel, this is because the hydrogen vessel has larger heat content and takes more time cool to ambient. Is this correct?

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  • $\begingroup$ Please fix the formatting; this question is unreadable. Use MathJax. Here’s a MathJax tutorial. Also, please do not use uncommon acronyms. What is "HTC" ? $\endgroup$
    – garyp
    Sep 25, 2016 at 2:21

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Yes, it takes more energy (heat is a type of energy) to heat up the substance with the greater heat capacity, all other things (such as $\Delta T$, and mass) being equal.

If both substances have the same heat transfer coefficient (measured in units of power per unit temperature per unit area), then the one with the greater heat capacity will cool down more slowly, all other things (critically geometry of container) being equal. This is because more energy must be lost from the substance of greater heat capacity to drop the temperature. To lose more energy, it takes more time.

Heat capacities and heat transfer coefficients are themselves temperature dependent quantities, so my answers are only valid for modest $\Delta T$. For example, the heat capacity of hydrogen gas changes in very interesting ways as you get to really low temperatures, due to the equilibrium ratio of ortho/para hydrogen (both hydrogen, but with different nuclear spin states).

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