Solving a Heat/Energy Problem: Final Temp of Steam

[PHYclueless]

Hello all. I have two questions I need help with but I'll post them in separate posts. I'll attach the problem and the work I've attempted. If someone could give me another idea I'd appreciate it. Thank you!

To make steam, you add 5.6x10^5J of heat to .220kg of water at an initial temperature of 50c. Find the final temperature of the steam, assuming a specific heat for steam = 2010J/(kg K), latent heat of fusion for water=33.5x10^4J/kg, and a latent heat of vaporization =22.6x10^5J/kg.

This is what I started working on and my answer comes out to be 38 degrees but the true answer is 138. Not sure where I'm going wrong here.

mass(specific heat)(change in temp)+mass(latent fusion)+mass(specific heat)(Tf-Ti)+mass(latent vaporization)=Energy

.220kg(4186J/kgc)(50c)+.220kg(33.5x10^4J/kg)+.220kg(4186J/kgc)(Tf-100c)+.220kg(22.6x10^5)=5.6x10^5J

Thanks!

 

[lightgrav]

That's because you "melted" your 50 degree (hot) water.

 

[Andrew Mason]

Hello all. I have two questions I need help with but I'll post them in separate posts. I'll attach the problem and the work I've attempted. If someone could give me another idea I'd appreciate it. Thank you!

To make steam, you add 5.6x10^5J of heat to .220kg of water at an initial temperature of 50c. Find the final temperature of the steam, assuming a specific heat for steam = 2010J/(kg K), latent heat of fusion for water=33.5x10^4J/kg, and a latent heat of vaporization =22.6x10^5J/kg.

This is what I started working on and my answer comes out to be 38 degrees but the true answer is 138. Not sure where I'm going wrong here.

mass(specific heat)(change in temp)+mass(latent fusion)+mass(specific heat)(Tf-Ti)+mass(latent vaporization)=Energy

.220kg(4186J/kgc)(50c)+.220kg(33.5x10^4J/kg)+.220kg(4186J/kgc)(Tf-100c)+.220kg(22.6x10^5)=5.6x10^5J

What does the latent heat of fusion have to do with this problem? What state is the water in initially? What happens when heat is added?

You have to apply your knowledge of physics to derive the correct expression first and be able to explain it.

I suggest you work out the equation for temperature change and then plug in the numbers.

AM

 

[Pengwuino]

Do you really think the water will become cooler if you add heat to it? I suggest you first determine, using the specific heat, if the energy added will be enough to make it vaporize. If so, determine how much energy is left over for when you change from 50-100 degrees. Then determine if all the water will vaporize with the left-over energy there. From there you can use another specific heat to determine how much the steam heats up. Remember that your equation will change at every stage since the specific heats will change. 1 equation will not solve this.