Answer:
Amount of required rations ≥ 15 g
Other assumptions made:
1. All the energy released from the rations is converted to heat
2. All the rations is completely metabolized to release energy
3. No other heat losses occur in the body except due to wetness of her clothing.
Explanation:
Using H = mcθ
where m is mass of the hiker in Kg,
c is specific heat capacity of water/hiker = 4200 JKg⁻¹K⁻¹
θ is temperature change in K
Note : heat capacity of water = specific heat capacity x molar mass
specific heat capacity = heat capacity / molar mass
c = 75.348 JK⁻¹mol⁻¹/18 x 10⁻³ Kgmol⁻¹ = 4186 JKg⁻¹K⁻¹ ≅ 4200 JKg⁻¹K⁻¹
Heat lost, H = 50.0 Kg x 4200 JKg⁻¹K⁻¹ x 2.5 K
H = 5.25 x 10⁵ J = 525 KJ
To avoid this heat loss, the hiker must consume enough emergency rations that releases heat equal to or greater than the heat loss due to wetness of her clothing.
Energy per gram of rations = 35 KJ
Amount of required rations ≥ 525 KJ / 35 KJ/g
Amount of required rations ≥ 15 g
Therefore, the hiker must consume 15 g or more of her emergency rations.
Other assumptions made:
1. All the energy released from the rations is converted to heat
2. All the rations is completely metabolized to release energy
3. No other heat losses occur in the body except due to wetness of her clothing.
