Question

A 56-kg hiker is climbing the 828-m-tall Burj Khalifa in Dubai. If the efficiency of converting the energy content of the bars into the work of climbing is 25%, the remaining 75% of the energy released through metabolism is heat released to her body. She eats two energy bars, one of which produces 1.10×103kJ of energy upon metabolizing. Assume that the heat capacity of her body is equal to that for water (75.3 Jmol−1⋅K−1). Calculate the increase in her temperature at the top of the structure.

Answer 1

The given question is incomplete. The complete question is as follows.

A 56-kg hiker is climbing the 828-m-tall Burj Khalifa in Dubai. If the efficiency of converting the energy content of the bars into the work of climbing is 25%, the remaining 75% of the energy released through metabolism is heat released to her body. She eats two energy bars, one of which produces 1.10×103kJ of energy upon metabolizing. Assume that the heat capacity of her body is equal to that for water (75.3 Jmol−1⋅K−1). Calculate the increase in her temperature at the top of the structure.

Calculate the temperature at the top of the structure. Assume her intitial temperature to be
`36.6^(o)C`.

Step-by-step explanation:

Energy present in total of two bars is as follows.

`2 * 1.2 * 10^(3) kJ`

`2.4 * 10^(3)` kJ

`2.4 * 10^(6) J` (as 1 kJ = 1000 J)

As 75% of energy releases out. Let us assume that energy releases out of its body be E. Then, energy will be calculated as follows.

E =
`(75)/(100) * 2.4 * 10^(6) J`

=
`180 * 10^(4)` J

Given data is as follows.

mass (m) = 56 kg

= 56000 g (1 kg = 1000 g)

Specific heat = 4.18
`J/g ^(o)C`

As heat is releasing which means that value of E will be negative.

-E =
`mC (T_(2) - T_(1))`

`-(180 * 10^(4) = 56000 g * 4.18 * (T_(2) - 36.6)^(o)C`

`T_(2) = 28.74^(o)C`

Her temperature at the top of the structure is
`28.74^(o)C`.

Now, change in temperature is calculated as follows.

`\Delta T = (36.6 - 28.74)^(o)C`

=
`7.86^(o)C`

Thus, we can conclude that increase in her temperature at the top of the structure is
`7.86^(o)C`.