Latent Heat Question: Calculate Vaporization Rate & Energy Needed

[Bgerst103]

Homework Statement

A scientist heats up a substance by applying heat at a constant rate of 75 J/s. She measures that
it takes 1 minute for 100 grams of the substance to evaporate. What is the latent of vaporization
of this substance? If she starts with 1 kg of the substance, how long will it take for it to
evaporate and how much energy will it take to evaporate the substance?

Homework Equations

Q=mL?

3. The Attempt at a Solution [/b

I'm not really sure how to use Q=mL. Does 75 J/s go into Q or is Q the total amount of joules. I know m is the mass and L is the specific latent heat.

 

[adjacent]

Homework Statement

A scientist heats up a substance by applying heat at a constant rate of 75 J/s. She measures that
it takes 1 minute for 100 grams of the substance to evaporate. What is the latent of vaporization
of this substance?

I will use the formula $E=mL_v$ for easiness.
J/s is the unit of power so if you know the power and the time,you should be able to find the energy supplied.
Use$E=mL_v$ to find the $L_v$.

 

[Bgerst103]

I will use the formula $E=mL_v$ for easiness.
J/s is the unit of power so if you know the power and the time,you should be able to find the energy supplied.
Use$E=mL_v$ to find the $L_v$.

So, 75 x 60 is equal 4500. 4500= (.1kg)(L) -> L=45000. If it takes 1 minute to vaporize 100g it should take 10 minutes for a kg and 45000 J?

 

[adjacent]

So, 75 x 60 is equal 4500. 4500= (.1kg)(L) -> L=45000. If it takes 1 minute to vaporize 100g it should take 10 minutes for a kg and 45000 J?

Correct.

 

[HalfLostAndSearching]

Hello,

To calculate the vaporization rate, we can use the formula Q/t, where Q is the amount of energy and t is the time. In this case, Q = 75 J/s and t = 1 minute = 60 seconds. Therefore, the vaporization rate is Q/t = 75 J/s / 60 s = 1.25 J/s.

To calculate the energy needed to evaporate 100 grams of the substance, we can use the formula Q = mL, where m is the mass and L is the specific latent heat. We know that the mass is 100 grams = 0.1 kg. We can rearrange the formula to solve for L: L = Q/m = (75 J/s)(60 s) / 0.1 kg = 45,000 J/kg.

If we start with 1 kg of the substance, it will take 10 times longer to evaporate (since we have 10 times the mass). Therefore, it will take 10 minutes and the total energy needed will be 10 times higher, which is 450,000 J.

I hope this helps! Let me know if you have any further questions.