BY HOW MANY DEGREES OF CELSIUS WOULD THE TEMPERATURE OF 100 GALLONS OF WATER INCREASE IF 300 CALORIES WERE ADDED TO IT?
change 100 gallons of water to mass of water.
then
heat=masswater*specific heat water*changeinTemp
To determine the increase in temperature of 100 gallons of water when 300 calories are added to it, we need to use the specific heat capacity of water. The specific heat capacity of water is approximately 1 calorie/gram °C.
Here's the step-by-step process to calculate the increase in temperature:
1. Convert the volume of water from gallons to grams:
- 1 gallon = 3,785.41 grams (approx.)
- 100 gallons ≈ 378,541 grams
2. Calculate the heat energy transferred:
- Heat energy transferred (in calories) = Mass of water (in grams) × Specific heat capacity of water (in calorie/gram °C) × Change in temperature (in °C)
- Mass of water = 378,541 grams
- Specific heat capacity of water = 1 calorie/gram °C
- Change in temperature is what we are trying to find.
Now, we rearrange the formula to solve for the change in temperature:
- Change in temperature = Heat energy transferred / (Mass of water × Specific heat capacity of water)
- Change in temperature = 300 calories / (378,541 grams × 1 calorie/gram °C)
Calculating the result:
- Change in temperature = 0.000792 °C
Therefore, the temperature of 100 gallons of water would increase by approximately 0.000792 degrees Celsius when 300 calories are added to it.