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The chemical energy in food is calculated by determining the heat transferred to a small body of water when that piece of food is combusted. Calculate the nutritional calories in a potato chip that raises the temperature of 70.855 g of water by [tex]$7.47^{\circ} C$[/tex].

[tex]\[\square\][/tex]


Sagot :

To determine the nutritional calories in a potato chip that raises the temperature of 70.855 grams of water by 7.47°C, we follow these steps:

1. Identify the given data:
- Mass of water: [tex]\( 70.855 \)[/tex] grams
- Temperature change: [tex]\( 7.47 \)[/tex]°C
- Specific heat capacity of water: [tex]\( 4.186 \)[/tex] J/g°C

2. Calculate the amount of energy absorbed by the water in joules:
The formula to find the heat energy absorbed or released by a substance is:
[tex]\[ Q = m \cdot c \cdot \Delta T \][/tex]
where:
- [tex]\( Q \)[/tex] is the heat energy in joules (J)
- [tex]\( m \)[/tex] is the mass of the substance in grams (g)
- [tex]\( c \)[/tex] is the specific heat capacity (for water, it is [tex]\( 4.186 \)[/tex] J/g°C)
- [tex]\( \Delta T \)[/tex] is the change in temperature in Celsius (°C)

Substituting the given values:
[tex]\[ Q = 70.855 \, \text{g} \cdot 4.186 \, \text{J/g°C} \cdot 7.47 \, \text{°C} \][/tex]

3. Compute the energy in joules:
[tex]\[ Q = 2215.5947541 \, \text{J} \][/tex]

4. Convert the energy from joules to nutritional calories:
One nutritional calorie (also called a "large calorie" or kilocalorie) is equal to 4184 joules. Therefore, to convert joules to nutritional calories, we use the conversion factor:
[tex]\[ 1 \, \text{calorie} = 4184 \, \text{joules} \][/tex]

Hence, the energy in nutritional calories is:
[tex]\[ \text{Calories} = \frac{Q}{4184} \][/tex]
Substituting the calculated joules:
[tex]\[ \text{Calories} = \frac{2215.5947541 \, \text{J}}{4.184} = 529.53985519 \, \text{calories} \][/tex]

Therefore, the nutritional calories in the potato chip are approximately [tex]\( 529.54 \)[/tex] calories.