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Under any thermodynamical change, U = Q + W. where U is the internal energy of the system (function of state), Q is the heat added to the system and W the work done on the system†. According to the first law we thus have Qsurr = Q and Wsurr = W , where the subscript ‘surr’ indicates the system’s surroundings.
The quantitative relationship between heat transfer and temperature change contains all three factors: Q = mcΔT, where Q is the symbol for heat transfer, m is the mass of the substance, and ΔT is the change in temperature. The symbol c stands for specific heat and depends on the material and phase.
The equation for heat transfer Q is. Q = m c Δ T, 11.7. where m is the mass of the substance and Δ T is the change in its temperature, in units of Celsius or Kelvin. The symbol c stands for specific heat, and depends on the material and phase. The specific heat is the amount of heat necessary to change the temperature of 1.00 kg of mass by 1.00 ºC.
Use the equation for heat transfer \(Q = mc\Delta T\) to express the heat lost by the aluminum pan in terms of the mass of the pan, the specific heat of aluminum, the initial temperature of the pan, and the final temperature: \[Q_{hot} = m_{A1}c_{A1}(T_f - 150^oC). \nonumber\]
Heat, which is energy transferred into or out of a system, can be transformed into (or come from) some combination of a change in internal energy of the system and the work done by (or on) the system.
Newton’s law of heating models the average temperature in an object by a simple ordinary differential equation, while the heat equation is a partial differential equation that models the temperature as a function of both space and time.
Its principles constitute the laws of thermodynamics and these laws govern all phenomena in the physical universe and are in particular applied to situations where exchanges in heat and changes in entropy are relevant.
