Thermal physics

Heat and specific heat capacity

Heat that changes temperature is Q=mcΔT; specific heat capacity measures how difficult it is to warm a unit mass.

When a body absorbs heat without changing phase, its temperature usually rises; it usually falls when heat is released. Mass and material affect the heat required.

Heat exchange

In an insulated system, heat lost by the warm body equals heat gained by the cooler one. Without a phase change: $m_1c_1(T_1-T_f)=m_2c_2(T_f-T_2)$; the final temperature lies between the initial values.

Quick check

The relation $Q=mc\Delta T$ gives the energy transferred when temperature changes without a phase change. Doubling the mass doubles the required heat for the same substance and temperature rise; a material with larger specific heat capacity requires more energy. This is why sand warms faster than water in the same sunshine, while water can store substantial thermal energy. In a mixing problem, first identify which object releases heat and which absorbs it, then write an energy balance. For an insulated container with negligible container heat capacity, the signed heats add to zero. In a real experiment, some energy warms the container or escapes to the surroundings, so the measured final temperature may differ from the ideal prediction. Convert grams to kilograms and check the units of $c$ before calculating.

For example, warming 0.20 kg of aluminum by 15 K with $c=900$ J kg⁻¹ K⁻¹ requires $Q=2700$ J. Water needs more energy for the same temperature rise because its specific heat capacity is larger. The calculation shows why the material and the no-loss assumption must be stated; mass and temperature change alone are not enough.