Question

A serving of Cheez-Its releases 1.30 x 10^4 kcal (1 kcal = 4.18 kJ) when digested by your body. If this same amount of energy were transferred to 1.75 mg of water at 35˚C, what would the final temperature be?

Answer 1

The final temperature is:- 7428571463.57 °C

Step-by-step explanation:

The expression for the calculation of heat is shown below as:-

`Q=m* C* \Delta T`

Where,

`Q` is the heat absorbed/released

m is the mass

C is the specific heat capacity

`\Delta T` is the temperature change

Thus, given that:-

Mass of water = 1.75 mg = 0.00175 g ( 1 g = 0.001 mg)

Specific heat of water = 4.18 J/g°C

Initial temperature = 35 °C

Final temperature = x °C

`\Delta T=(x-35)\ ^0C/tex] </p><p>Q = [tex]1.3* 10^4` kcal

Also, 1 kcal = 4.18 kJ =
`4.18* 10^3` J

So, Q =
`1.3* 10^4* 4.18* 10^3` J = 54340000 J

So,

`54340000=0.00175* 4.18* (x-35)`

`0.00175* \:4.18\left(x-35\right)=54340000`

`x-35=(54340000)/(0.007315)`

`x=7428571463.57`

Thus, the final temperature is:- 7428571463.57 °C