# How long does it take to heat a vessel?

• Modrisco89
In summary, the conversation discusses finding the time it takes to heat a vessel of water with specific heat capacity, density, volume, heat capacity of the vessel, and power rating of the element provided. The initial attempt at a solution uses the formula t=C(ΔT)/power and the Newton's law of cooling equation to calculate the time with and without taking into account ambient temperature. However, it is pointed out that the analysis is incorrect due to not considering the thermal inertia of water. The correct solution is requested before attempting to solve the problem with heat loss to the surrounding air included.
Looks like I'm not out tench yet, so I'm assuming it should be in watts per kelvin for the k value, thermal conductance of air perhaps?

I found kA/L

So k = air thermal conductance and A = surface area of tank, what would L be?

Modrisco89 said:
Looks like I'm not out tench yet, so I'm assuming it should be in watts per kelvin for the k value, thermal conductance of air perhaps?
Start with a value of k equal to the surface area times 10 ##\frac{W}{m^2.C}##.

Chestermiller said:
Start with a value of k equal to the surface area times 10 ##\frac{W}{m^2.C}##.

That's perfect; my values are coming out longer than the original equation I had for time, thank very much for all the help and sorry for my maths

Can I ask one question, when you solved that DE, what were your initial conditions? I assumed it to be T(0) would it be something else? like k(Ta-To)?

Last edited by a moderator:
Modrisco89 said:
Can I ask one question, when you solved that DE, what were your initial conditions? I assumed it to be T(0) would it be something else? like k(Ta-To)?
The initial condition is ##T=T_0## at time t = 0.

Modrisco89 said:
Can I ask one question, when you solved that DE, what were your initial conditions? I assumed it to be T(0) would it be something else? like T(0)-Ta?
Chestermiller said:
The initial condition is ##T=T_0## at time t = 0.
Ya I thought that made sense, I'll have to double triple check my maths and find out why the LTM is not working for me, thanks

Marking as solved

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