Question

The energy density in a pellet of algae is determined by a bomb calorimetry technique,in which the food is burned (in an oxygen rich environment) and the amount of heat transfer ismeasured. How many joules of energy per kilogram are there in dried algae if when burning a5.00 g algae pellet, and transferring this energy to 0.500 kg of water held in a 0.100 kg aluminumcup, a 54.9oC temperature increase is observed? The specific heat of water is 4186 J/(kg K) andthe specific heat of aluminum is 900 J/(kg K)

Answer 1

The value is
`E =  2.396 *10^(7) \  J/kg`

Step-by-step explanation:

From the question we are told that

The specific heat of water is
`c_w =  4186 \  J/(kg \cdot K)`

The specific heat of aluminum is
`c_a  =  900 \  J/(kg \cdot K)`

The temperature increase is
`\Delta  T  =  54.9^oC`

The mass of water is
`m_w =  0.500 \  kg`

The mass of the aluminum is
`m_a  =  0.100 \ kg`

The mass of the algae pellet is
`m  =  5.00 \  g  =  0.005 \  kg`

The heat transfer is mathematically represented as

`Q =  (m_w * c_w + m_a *  c_a) \Delta  T`

=>
`Q =  (0.5 * 4186 +  0.1 * 900) *  54.9`

=>
`Q =  119847 \  J`

Generally the energy generated per kilogram of dried algae is mathematically represented as

`E = (Q)/(m)`

=>
`E =  (119847)/(0.005)`

=>
`E =  2.396 *10^(7) \  J/kg`