To address your question, let's break down the concepts of heat transfer, work done, and the implications of a thermally insulated system. When you rub a solid box, friction generates heat, which can indeed affect the temperature of the gas inside. However, the way we analyze this situation depends on the definitions of work (W) and heat (Q) in thermodynamics.
Understanding Heat Transfer and Work
In thermodynamics, heat (Q) refers to energy transferred due to temperature differences, while work (W) is energy transferred when a force is applied over a distance. When you rub the box, the friction converts mechanical energy into thermal energy, which raises the temperature of the gas inside. This process can be considered as work being done on the system, leading to an increase in internal energy.
Thermally Insulated Systems
Now, regarding your specific example with the thermally insulated copper vessel containing water: when you shake the vessel vigorously, you are indeed doing work on the water. This work increases the kinetic energy of the water molecules, which translates into a rise in temperature. The key point here is that even though the vessel is thermally insulated, the work done on the system can still result in a temperature change.
- First Law of Thermodynamics: This principle states that the change in internal energy (ΔU) of a system is equal to the heat added to the system (Q) minus the work done by the system (W): ΔU = Q - W.
- In a thermally insulated system: Since no heat is exchanged with the surroundings (Q = 0), any increase in internal energy must come from work done on the system (W > 0).
Applying the Formula
When you apply the formula dQ = mc dT, you are calculating the heat transfer based on the mass (m), specific heat capacity (c), and the change in temperature (dT). In a thermally insulated system, the heat transfer (Q) is indeed zero, but the work done (W) is what causes the temperature to rise. Thus, the formula is not wrong; it simply reflects that the energy input comes from work rather than heat transfer from the environment.
Conclusion
In summary, when the copper vessel is shaken, the work done on the water increases its internal energy, leading to a rise in temperature, despite the system being thermally insulated. The formula dQ = mc dT is applicable, but in this context, it’s important to recognize that the heat transfer is zero, and the temperature change is due to the work done on the system. This distinction is crucial in thermodynamics and helps clarify how energy transformations occur within closed systems.
