Jim has an aqarium that holds 4,000 mL of water. It is at the room's temerature of 20 degrees Celsius. How many calories need to be transferred to the water for it to reach 25 degrees Celsius?
To calculate the number of calories needed to transfer to the water, we can use the specific heat capacity formula:
q = m * c * ΔT
where:
q = energy transferred (calories)
m = mass of the water (grams)
c = specific heat capacity of water (1 calorie/gram °C)
ΔT = change in temperature (°C)
First, we need to determine the mass of the water. We know that 1 mL of water has a mass of 1 gram. Since the aquarium holds 4,000 mL of water, the mass of the water is 4,000 grams.
Next, we can substitute the values into the formula:
q = 4,000 g * 1 cal/g °C * (25 °C - 20 °C)
Simplifying the equation:
q = 4,000 g * 1 cal/g °C * 5 °C
q = 20,000 cal
Therefore, 20,000 calories need to be transferred to the water for it to reach 25 degrees Celsius.