Solving the Hardest Thermal Process Question: Find W/Q Ratio

[Dooh]

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.

 

[Meir Achuz]

Q=cm delta T seems right. Did you convert calories to Joules?

 

[quicknote]

I understand the frustration and difficulty of trying to solve complex thermodynamic problems. In order to solve this particular question, we need to first clarify the meaning of Q. In thermodynamics, Q represents the heat absorbed or released by a system during a process. In this case, Q would represent the heat absorbed by the water as it is heated in the open pan.

To find the W/Q ratio, we need to calculate both W and Q. As you correctly stated, W can be calculated using the equation W = P(Vf - Vi), where P is the pressure and Vf and Vi are the final and initial volumes of the water, respectively. However, in order to calculate Q, we need to use the specific heat capacity of water (c) and the change in temperature (delta T) of the water.

To find the change in temperature, we can use the ideal gas law, PV = nRT, where n is the number of moles of water and R is the gas constant. Since the water remains a liquid, we can assume that n and R remain constant and therefore, PV is directly proportional to T. This means that as the volume of the water increases due to expansion, the temperature will also increase.

Once we have calculated Q, we can then divide W by Q to find the W/Q ratio. This ratio will give us an understanding of the efficiency of the process, as it represents the amount of work done by the water compared to the amount of heat absorbed.

In conclusion, solving this thermal process question requires a combination of understanding thermodynamic principles and utilizing equations to calculate the necessary values. I hope this explanation helps in your understanding and approach to solving this challenging problem.