Solve Hard Thermodynamics Q: Find Water W/Q Ratio

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The discussion centers on a challenging thermodynamics problem involving the work done by water in an open pan at 1 atm pressure. The key equation to solve the problem is W/Q, where W is calculated as P(Vf - Vi). The original poster struggles to determine the correct value for Q, initially attempting Q = cm delta T but realizing it was incorrect. There is a suggestion that specific heat capacity should be considered using c_p instead. Clarification on these concepts is sought to accurately solve the problem.
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This question is considered one of the hardest in this chapter regarding thermodynamics. I spent countless time trying to figure it out but i was never close to the answer. The question is:

Water is heated in an open pan where the air pressure is 1atm. WAter remains a liquid but expanded by a small amount when it was heated. FIND THE RATIO OF WORK DONE BY WATER TO THE HEAD ABSOBED BY THE WATER.

So that means:

W / Q

where W = P(Vf - Vi)
but what's Q? I tried Q = cm delta T but i was wrong. if anyone can help me i'd appreciate it thanks.
 
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What is cm? Shouldn't you be using c_p?
 

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