Specific Heat at High Pressure

I am wondering if increasing the pressure on water would have any effect on the amount of heat required to increase temperature of water by say 1'C.

So Q(heat added) = C(specific heat) * m(molar mass) * t( change in temperature) [Can read more here: http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/spht.html]

In the above mentioned equation, would you know what changes if one increases/decreases pressure on the system?

My thinking is, since at low pressure molecules will have more intermolecular space to move it would be easier for them to absorb heat and move rapidly and under high pressure molecules will be close to each other thus more heat will be required to increase temperature.

What do you guys think? Thank you for sharing your wisdom.

Thanks