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On particle level, temperature is a measure of the kinetic energy of the particles. By increasing the temperature, the particles hit the "walls" of the marshmallow with greater force, forcing it to expand.

On mathematical level, Charles states:

$V_1/T_1=V_2/T_2$

Multiply with $T_2$

$V_2=T_2*V_1/T_1$

Since volume and temperature can not take negative values, $V_2$ is proportional to the temperature rise, thus increasing when temperature is increased.

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