Convert Joules to Calories - 1 cal = 4.184 J

[olop4444]

Homework Statement

1 calorie is the energy needed to raise the temperature of 1 gram of water by 1 degree celsius, i.e., the specific heat of water is 1 calorie/g-°C. How many joules is 1 calorie?

Homework Equations

ΔU = nαkΔT

The Attempt at a Solution

I attempted to use equipartition to solve this problem.
α of water should be 6*1/2 = 3.
1 gram of water should have 6.02*10^23 * 1/18 = 3.34 * 10^22 molecules
So to increase the temperature of 1 gram of water by 1° C or K, I obtained 3.34*10^22*3*1.38*10^-23*1 = 1.38 J.

However, it is well established that 4.184 J = 1 calorie. What am I doing wrong?

 

[ehild]

Homework Statement

1 calorie is the energy needed to raise the temperature of 1 gram of water by 1 degree celsius, i.e., the specific heat of water is 1 calorie/g-°C. How many joules is 1 calorie?

Homework Equations

ΔU = nαkΔT

The Attempt at a Solution

I attempted to use equipartition to solve this problem.
α of water should be 6*1/2 = 3.
1 gram of water should have 6.02*10^23 * 1/18 = 3.34 * 10^22 molecules
So to increase the temperature of 1 gram of water by 1° C or K, I obtained 3.34*10^22*3*1.38*10^-23*1 = 1.38 J.

However, it is well established that 4.184 J = 1 calorie. What am I doing wrong?

Welcome to PF!

Water behaves peculiarly when heated. It is because of its hydrogen bonds. The molecules not only vibrate around their equilibrium positions, but the hydrogen bonds also perform different coupled vibrations. These vibrations are excited more and more between zero and 100 °C. Water has much more degrees of freedom as 6 per molecule. The bonds can also break at higher temperatures, and that also consumes energy. All these result in heat capacity considerably larger than expected.

ehild

 

[olop4444]

Interesting. I guess I'll learn more about that later in the course. Thanks for your help!