If a cup of coffee is at 90°c and a person with a body temperature of 36°c touches it, how will heat flow between them?

According to II law of thermodynamics the heat always transfers from high temperature to low temperature body without aid of any external energy. So, according to this law the heat transfers from cup of coffee to the person body until both bodies reaches to the equilibrium state.

After attaining the equilibrium state, the heat transfer may be ceases between the bodies.

Whenever the person touches the hot coffee, he senses the heat that means the heat is transferring in to his body.

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what experimental evidence led scientists to change from the previous model to this one?

a few of the positive particles aimed at a gold foil seemed to bounce back.

the colors of light emitted from heated atoms had very specific energies.

experiments with water vapor showed that elements combine in specific proportions.

cathode rays were bent in the same way whenever a magnet was brought near them.