# Thermal Conductivity and latent heat

**1. The problem statement, all variables and given/known data**

If a copper kettle has a base of thickness 2.0mm and an area 3.0 x 10^{-2} m^{2} estimate the steady difference in temperature between the inner and outer surface of the base which

must be maintained to enable enough heat too pass through so that the temperature of 1 kg of water

rises of 0.25 K/s assume that there are no heat losses.

(ii) After reaching the temperature of 373K the water is allowed to boil under the same conditions for 120 seconds and the mass of water remaining in the kettle is 0.948kg.

Deduce a value for the specific latent heat of vaporization of water ( neglecting condensation of the steam in the kettle)

**2. Relevant equations**

Thermal conductivity of copper 3.8 x 10^{2} W/m/C

Specific Heat Capacity of water 4.0 x 10^{3} J/kg/K

Equations used

dQ/dt = kA(dΘ/dx)

where dQ/dt = rate of flow of heat

K = Thermal Conductivity

A = Area

dΘ = Change in Temperature

dx = Thickness

whereby dΘ/dx = Temperature gradient

Q = mCT

Where Q = Heat require

m = Mass of substance

C = Specific heat capacity

T = Temperature

Q= mL

Where Q = Heat Require

m = Mass

L = Latent Heat

**3. The attempt at a solution**

Firstly i used the specific heat capacity equation to find the rate of flow of heat

Q = 1 (4.0 x 10^{3} J/kg/K ) 0.25 K/s

= 1050 J/s

Using the above answer i substitute it into the equation for thermal conductivity

1050 = 3.8 x 10^{2} W/m/C (3.0 x 10^{-2} m^{2} )(dΘ/0.002m)

by simple calculations my answer = 0.18 degrees

Part (ii)

I am abit lost as to where to go from here… but im thinking i will have to multiply 120 seconds by 0.25K/s which = 30 K/s

Ok im lost!!!…:confused:

By the way is my answer correct for Part (i) ??

http://ift.tt/1q15J53

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