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.
