Thermal Conduction Homework: Find Rod's Conductivity

[Joshb60796]

Homework Statement

A rod, with sides insulated to prevent heat loss, has one end immersed in boiling water at 100C and the other end immersed in a water/ice mixture at 0C. The rod has uniform cross-sectional area of 4.04 cm^2 and length 91cm. Under steady state conditions, heat conducted by the rod melts the ice at a rate of 1.0g every 34 seconds. What is the thermal conductivity of the rod?

Homework Equations

H=dQ/dt=k*Area(TempChange)(1/length)
Heat of Fusion of water is 3.34*10^5 J/kg

The Attempt at a Solution

(3.34*10^5*91)/(34seconds*100C*4.04cm^2) = 2200

My answer key says 220 W/m*K, I've tried converting 91cm to .91m and 4.04cm^2 to .000404m^2 and I get the same 2200 answer. I think I'm making a conversion error but I'm not sure, please advice, thank you.

 

[technician]

have you realized that it is 1x10^-3 kg melted in 34secs

 

[cepheid]

Your work is off by a factor of 1000 because you forgot to multiply the heat of fusion of water (J/kg) by the rate at which mass is melting (0.001 kg). Only 334 J of heat is being transferred in 34 sec, NOT 334,000 J.

 

[Joshb60796]

hmm I believe I follow what you are saying. I recalculated with 334J and my answer comes to 2.20 but that's still not what the answer key says. Am I just dense or is maybe the key incorrect?

 

[Joshb60796]

wait, maybe the 2.20 is in W/cm*K and the 220 on the key is W/m*K? ...nevermind, that would be backwards

 

[cepheid]

I don't know what to tell you, because it's just arithmetic at this point. You are messing it up somewhere and just need to be meticulous and get it right.

 

[Chestermiller]

Homework Statement

A rod, with sides insulated to prevent heat loss, has one end immersed in boiling water at 100C and the other end immersed in a water/ice mixture at 0C. The rod has uniform cross-sectional area of 4.04 cm^2 and length 91cm. Under steady state conditions, heat conducted by the rod melts the ice at a rate of 1.0g every 34 seconds. What is the thermal conductivity of the rod?

Homework Equations

H=dQ/dt=k*Area(TempChange)(1/length)
Heat of Fusion of water is 3.34*10^5 J/kg

The Attempt at a Solution

(3.34*10^5*91)/(34seconds*100C*4.04cm^2) = 2200

My answer key says 220 W/m*K, I've tried converting 91cm to .91m and 4.04cm^2 to .000404m^2 and I get the same 2200 answer. I think I'm making a conversion error but I'm not sure, please advice, thank you.

(334*0.91)/(34seconds*100C*.000404) = 221

 

[Joshb60796]

Thank you Chester, I'd been messing with this over and over and apparently it's like trying to grammar check your own novel, I never tried both converting to meters, and fixing my gram and kilogram mistake. Thank you so much :) I don't know how I missed it now.