This application simulates heat exchange and thermal equilibrium between a liquid and a solid object with different initial temperatures.

Use your finger (if on a mobile device) or the mouse cursor (in the desktop version) to:

• Pull and release the spheres in "Thermal balance" mode.

Operating modes:

• Heating Mode: Simulates the rise in temperature of a liquid being heated with flames of variable power.
• Thermal Equilibrium Mode: shows the temporal evolution of the liquid and sphere temperatures until the final temperatures are approximately equal.

In both operating modes, the simulator takes into account the latent heat of vaporization and the liquid boiling process.

In "warm-up" mode, this simulation works based on the ODE solution

$ \dfrac{dT}{dt} = \dfrac{P}{m_lc}, \ \ \ \ \ \ \ T < T_{ebul.} $ $ \dfrac{dm_{vap}}{dt} = \dfrac{P}{L}, \ \ \ \ \ \ T = T_{ebul.}, $

where $T$ is the temperature of the liquid, $T_{ebul.}$ its boiling point, $m_l$ its mass, $c$ its specific heat, $L$ its latent heat of vaporization, $m_{vap}$ the mass of the vapor and $P$ the power of the flames.

In "thermal equilibrium" mode, the ODEs are as follows:

$ \dfrac{dT_l}{dt} = -k(T_l - T_e), $ $ \dfrac{dT_e}{dt} = \k(T_l - T_e), $

where $T_l$ is the temperature of the liquid, $T_e$ the temperature of the sphere and $k = 1$ s$^{-1}$ a constant.

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