A 0.25 g sample of a pretzel is burned. The heat it gives off is used to heat 50 g of water from 18°C to 42°C. What is the energy value of the pretzel, in kcal/g?
4.8 kcal per g of pretzel (assuming no heat losses during combustion)
The calculation assumes that all of the heat generated went into heating up the water; in reality that will never happen, although in a very well made calorimeter any losses will be reduced by efficient thermal lagging.
The energy used, E is equal to m.c.
Ths specific heat capacity of water under the conditions described is 1 kcal/K.kg , where K is the temperature in Kelvins, and kg is the mass.
So now we can work out the figures.
E = 0.05 x 1 x 24 = 1.2 kcal.
So we know that 0.25 g of pretzel gives off (assuming no losses) 1.2 kcal of heat energy, so per gram the energy would be (1/0.25) x 1.2 = 4.8 kcal.