167k views
1 vote
How many grams of water can be heated from 20.0°C to 75.0°C using 3500 calories?

a) 500 g
b) 750 g
c) 1000 g
d) 1250 g

User HSJ
by
7.6k points

1 Answer

2 votes

Final answer:

By converting 3500 calories to joules and using the heat equation (q = m × c × ΔT) with the specific heat capacity of water, it's determined that approximately 63.5 grams of water can be heated from 20.0°C to 75.0°C. None of the options provided in the question is correct.

Step-by-step explanation:

To determine how many grams of water can be heated from 20.0°C to 75.0°C using 3500 calories, we should first convert calories to joules since the specific heat capacity of water is usually given in joules per gram degree Celsius (J/g°C). Knowing that 1 calorie equals 4.184 joules, we can calculate the total energy in joules:

3500 cal × 4.184 J/cal = 14644 J

Next, we can use the formula q = m × c × ΔT, where q is the heat in joules, m is the mass in grams, c is the specific heat capacity (4.184 J/g°C for water), and ΔT is the temperature change in degrees Celsius.

Rearranging the formula to solve for the mass m gives us:

m = q / (c × ΔT)

Then substituting the known values:

m = 14644 J / (4.184 J/g°C × (75°C - 20°C))

m = 14644 J / (4.184 J/g°C × 55°C)

m = 14644 J / 230.62 J/g = 63.5 g (approximately)

Therefore, using 3500 calories, you can heat approximately 63.5 grams of water from 20.0°C to 75.0°C, which means none of the options (a, b, c, or d) listed in the question accurately reflect the correct answer.

User Rekle
by
8.4k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.