Generating stations 7

 Question  =  A generating station has an overall η of 15%  and 0.75 kg of coal is burnt per kwh by the station . Determine the calorific value of coal in kilocalories per kg ? 

Solution = let , 

» 1 kg be the calorific value of coal = x kcal , 

» 0.75 kg of coal by heat produced = 0.75 x kcal/ kg , 

» heat equivalent of 1 kwh = 860 kcal , 

» details of 860 kcal , 

( 1 kwh = 1000 watts × 3600 seconds = 36 ×10⁵ joules , 

» 4.18 joules = 1 calories ,  

» 1 joules = 1/4.18 calories ,  

» 36 ×10⁵ joules = ( 36 × 10⁵ j × 1c ) ÷ 4.18 j , = 860 ×10³ calories , or 860 kcal , )

»  η overall = electrical output heat unit / heat of combustion , 

» 0.15 = 860 kcal / 0.75 x kcal , = x = 860 /0.15 × 0.75 , = 7644.44 kcal/ kg , answer ✓