The foundation of thermodynamics is the distinction between “temperature” and “heat.” After clarifying the difference between everyday language and physics terminology, we will learn to handle specific heat and heat capacity quantitatively.
Basic Knowledge
Temperature (temperature) is a measure of how cold or hot an object is and corresponds to the average kinetic energy of its molecules. The SI unit is the kelvin [K], and its relationship with Celsius temperature is T [K] = t [℃] + 273.15。
Heat (heat) Q [J] is the amount of energy transferred between objects with a temperature difference.
Specific heat capacity (specific heat capacity) c [J/(kg·K)] is the amount of heat required to raise the temperature of 1 kg of a substance by 1 K.
Q = mcΔT (m: mass [kg], Δ T: temperature change [K])
Heat capacity (heat capacity) C [J/K] is the amount of heat required to raise the temperature of an entire object by 1 K. C = mc, Q = CΔT.
When objects A and B reach thermal equilibrium in an insulated container, the law of conservation of heat is: Qreleased = Qabsorbed.
Absolute temperature T [K] (temperature based on 0 K = −273.15 ℃, where molecular motion completely stops)
Specific heat c [J/(kg·K)] (a substance’s characteristic ease of heating; water has a large value of 4.2×10³ J/(kg·K))
Heat capacity C [J/K] (an object’s overall ability to store heat; C = mc)
Law of conservation of heat (in an insulated system, released heat = absorbed heat)
Thermal equilibrium (thermal equilibrium) (a state in which heat transfer between objects in contact has stopped and they have the same temperature)
Further Exploration (Background and Significance)
“Water has a high specific heat” has a profound effect on climate. Because the sea is difficult to warm and cool, coastal regions have a smaller annual temperature range than inland regions (maritime climate).
The unit cal (calorie) has also historically been used for heat. 1 cal = 4.19 J (Joule’s mechanical equivalent experiment). The “kcal” in food Calories refers to this.
Temperature measurement is based on the zeroth law of thermodynamics (if A and B are each in thermal equilibrium with object C, A and B are also in thermal equilibrium). This is the basis for the operation of thermometers.
In “heat-balance” problems often seen in entrance examinations, set up heat released by the hotter object = heat absorbed by the cooler object, express each using Q = mcΔT, and solve. When a phase change (melting or evaporation) occurs, it is necessary to add the latent heat term Q = mL.
- Temperature and heat are different physical quantities. Temperature = a state quantity; heat = transferred energy
- Q = mcΔT. c (specific heat) is characteristic of a substance; C (heat capacity) is characteristic of an object
- Insulated container: heat released by the hot object = heat absorbed by the cold object
- Use absolute temperature T = t + 273.15 in formulas
- When a phase change occurs, do not forget latent heat Q = mL
Points to Note (Common Confusions)
① Do not confuse specific heat (per unit mass) with heat capacity (for the entire object). ② “Higher temperature = more heat” is not generally true (the order can reverse when specific heat or mass differs). ③ Δ T has the same numerical value whether calculated in ℃ or K because it is a difference, but T itself must always use K. ④ When setting up the law of conservation of heat, it is safest to consistently take the released heat as positive.
Practice
- How many K does the temperature of a metal rise when 300 J of heat is supplied to 2.0 kg of metal with a specific heat of 0.50 kJ/(kg·K)?
- When a 500 g iron ball at 100 ℃ (specific heat 0.45 J/(g·K)) is placed in 1.0 kg of water at 20 ℃ (specific heat 4.2 J/(g·K)), find the thermal equilibrium temperature.
- What is an absolute temperature of 300 K in degrees Celsius?