yes Sarah, heat is low grade energy, but there is no missing heat, in reheat cycle we consume more heat to have more work.

Using heat from the boiler, or an economizer (heat exchanger equipment), you can increase net work = net Q by increasing total area for the T-s diagram, and hence as Mr. Fellah said, more heat is used for mechanical work.

For more info:

http://web.mit.edu/16.unified/www/SPRING/propulsion/notes/node66.html

Smith - Chemical Engineering Thermodynamics, 7th edition

Reheating as said earlier by Shoaib is used to improve the quality of steam at the end of there turbine section. Also we can have a secondary turbine thus getting more power and as we all know turbine efficiency increases as the enthalpy drop across the ends increases so by reheating we are increasing the enthalpy drop thereby increasing the turbine efficiency

Steam quality improvement contributes too, but the main effect come from temperature increase. Imagine the turbine with reheat as 2 independent turbines. After expansion in the 1st turbine steam can go to the second one either with or without additional heating (reheat). The higher the inlet temperature of the second turbine - the higher is its efficiency (like in regular Carnot cycle).

"The reheat cycle has been developed to take advantage of the increased efficiency with higher pressures, and yet avoid excessive moisture in the low pressure stages of the turbine". Book: Fundamentals of Classical Thermodynamics, 3rd edition, by Gordan J. Van Wylen and R. E. Sonntage, page 291.

I am sorry I did not see this question earlier. As usual, there are many good answers, but completeness is lacking. The main purpose of reheating is to avoid excess moisture in steam at the end of expansion to protect the turbine. But it need not improve the cycle efficiency. That will depend (as Dmitri said) upon whether the mean temperature of reheat addition is > or < the mean temperature of heat addition before reheat.

There are dozens of worked examples in various books on Thermodynamics and Power Plant Engineering. One of them might show a case where the reheat cycle efficiency is less than that without reheat.

You can find the best information at the web-page of Subrata Bhattacharjee:

"TEST: The Expert System for Thermodynamics". The vapou cycle simulation

applets can you help in an analysis of all important problems.

Jan Gorski, AGH Uni. Cracow, Poland

The reheat in the steam power cycle allows to improve its efficiency because any method causing a growth of an area of particular cycle is directly related to the obtainable work:

net work in power cycle = heat delivered - heat extracted.

Therefore another methods to improve an efficiency can be used:

- higher pressure (up tu supercritical parameters) and temperature of the steam at turbine entrance (limited only by an access to new materials),

- lower pressure in cindenser (but limited by vacum conditions),

- eliminating large heat losses (mixing the streams, heat recuperation, etc.).

Compare some examples using the Subrata applets.

In order to maintain the steam quality of nearly 0.84(good dryness fraction),reheat has to be adopted with maximum steam pressure at turbine inlet.in that case ,the steam after partial expansion in high pressure turbine (small in size) is returned back to boiler for reheating at constant pressure and then fed back to low pressure turbine(large in size).In case of two reheats, steam is super-heated twice at different constant temperatures.A high reheat pressure increases the the moisture content at turbine exhaust which results in scaling and it should be optimised.Thus the work produced is increased ,thereby efficiency increases.

By increasing the number of reheats, high steam pressures can be achieved but the mechanical stresses at higher rate than that of pressure, due to prevailing high temperature.Cost of fabrication may also increase.

For the reheat cycle, the exhaust steam from the high pressure turbine gains some heat either from the combustion gases leaving the boiler (if there is still much temperature difference) or by adding more heat by burning small amount of fuel. The energy of the exhaust steam with the gained heat increases the steam enthalpy of the steam and give a good opportunity to generate much work with the low pressure turbine. The two works (High pressure W_H and Low pressure W_L) are much greater than the heat added by fuel burned (Q1 and Q2), so the efficiency increases.

Another issue, the reheat helps in saving the turbine blades from corrosion due to low dryness fraction x

The ogre of bad expression is raising its head again and again in Research Gate. Though everybody might understand it, I am repeating it here for the sake of correct use of terminology. The blades of the steam turbine undergo EROSION due to high moisture content. Erosion is a mechanical action while the term Corrosion, so often confused with Erosion, is a chemical action. 

The phenomenon behind this can be described even more simple way. In reheating type boiler-turbine plant the heat/energy transferred into the steam per kilo is higher and enthalpy loss in condenser is relatively lower (it is always constant kJ/kg). One kilo of steam can work more. That also explains why it is more efficient to tap steam of low pressure part for condense preheating. The lower is the enthalpy loss in condenser compared to total heating&working power, the higher is the efficiency.