# How do you calculate the work of a Carnot Heat Engine using entropy?

The problem given is as follows:

A Carnot cycle has a heat engine fluid efficiency of 30%. The heat transfer to the fluid in the boiler Qh happens at 270 centigrade. At 270 centigrade, the entropy of saturated vapour and liquid water are 6.001KJ/(kgK) and 3.067KJ/(kgK), respectively. Determine the net work produced by the Carnot engine.

I am pretty sure to solve it you need to use the Carnot efficiency equation so 0.30 = W / Qh but I am not too sure how to get Qh from the information provided. Please explain or put me on the right track if you can!

Assuming reversible heat addition process: $$q = \int_{s_1}^{s_2} T \,ds = T \int_{s_1}^{s_2}ds=T\Delta s$$ $$w = \eta_{carnot} \,q$$