Heat transfer in polytropic process

[panu36912]

Homework Statement

A piston/Cylinder arrangement of initial volume 0.025 m³ contains saturated water vapor at 180 degree Celsius. The steam now expand in a Polytropic process with exponent n=1 to a final pressure of 200 kpa while it does work against the piston. Determine the heat transfer for this process.

Homework Equations

PVⁿ=constant

The Attempt at a Solution

I try solving this problem by using enthalpy.

Since state 1 is a saturated vapor, h₁= h_g=2778.16 kJ/kg

For state 2, its state is superheated vapor. By interpollating the value of h between 150 degree celsius and 200 degree celsius. I got the value of enthalpy equal 2829.79. Then i go for the heat transfer by using the formula, Q=m(h₂-h₁)

However, my answer is totally different from the answer key in the book. This problem is from Fundamental of Thermodynamic, Sontag and Borgnake, 8th edition, chapter 3, number 123.

The correct answer is 40.5 kJ .

 

[Chestermiller]

This approach is not correct. Is the heat transferred equal to the change in enthalpy if the pressure is not constant?

What is the initial pressure? What is the final pressure. What is the mass of water in the cylinder? How much work is done in the poly tropic process? What is the specific volume in the initial and final states? What is the final temperature, and on what basis did you determine it? What are the initial and final internal energies?

Chet