Thermodynamic systems, thermal equilibrium and the zeroth law
Systems are open, closed or isolated. The zeroth law: two bodies each in thermal equilibrium with a third are in equilibrium with each other.
Heat, temperature and thermodynamics
Rub your palms together and they warm up. Pump a bicycle tyre and the pump gets hot. In both, work produces heat. Thermodynamics studies heat, work and how energy changes from one form to another. Heat is energy that flows from one body to another because of a difference in temperature, always from the hotter to the colder body. A glass of cold water warms on a hot day, and hot tea cools on the table. The flow stops when both reach the same temperature. The unit of heat is the calorie. One calorie is the heat that raises 1 g of water from 14.5 °C to 15.5 °C. 1 cal = 4.18 J and 1 kcal = 10³ cal.
System, surroundings and thermodynamic variables
A thermodynamic system is the definite amount of matter we choose to study, such as the gas in a cylinder. It is enclosed by a boundary, which may be real or imaginary. Everything outside the boundary is the surroundings. We describe the state of a system by thermodynamic variables: pressure P, volume V and temperature T. A system is in thermodynamic equilibrium when it is in thermal, mechanical and chemical equilibrium together. Then P, V and T do not change with time.
Three kinds of system
| System | Mass crosses the boundary? | Energy crosses the boundary? | Example |
|---|---|---|---|
| Open | Yes | Yes | A water heater (geyser); milk boiling in an open pan |
| Closed | No | Yes | Gas in a cylinder fitted with a piston |
| Isolated | No | No | Tea in a good thermos flask (very nearly isolated) |
The zeroth law and the idea of temperature
- 1Take three bodies A, B and C. Keep A in contact with C until no more heat flows: A and C are now in thermal equilibrium.
- 2Separately, keep B in contact with C until they too are in thermal equilibrium.
- 3Now put A and B in contact. No heat flows between them.
- 4Zeroth law: if two systems are each in thermal equilibrium with a third, they are in thermal equilibrium with each other.
- 5★So, all bodies in thermal equilibrium share one property, called temperature. Body C acts as a thermometer: it tells whether A and B are equally hot without putting them together.
★ key step
Worked example: heat in calories and joules
How much heat is needed to warm 500 g of water from 25 °C to 75 °C? Give the answer in calories and in joules. (Heat to warm 1 g of water by 1 °C = 1 cal; 1 cal = 4.18 J)
- Rise in temperature = 75 °C − 25 °C = 50 °C.
- Heat = mass × 1 cal g⁻¹ °C⁻¹ × rise = 500 g × 1 × 50 °C = 25000 cal = 25 kcal.
- In joules: 25000 cal × 4.18 J cal⁻¹ = 104500 J.
25 kcal, or about 1.05 × 10⁵ J
A thermos flask keeps tea hot for hours because it is nearly an isolated system. A clinical thermometer works by the zeroth law: it shows your temperature once it reaches thermal equilibrium with your body.
2 marks: “Say whether each is an open, a closed or an isolated system, with a reason: (a) a pressure cooker with its whistle blowing, (b) gas sealed in a cylinder with a piston, (c) hot tea in a good thermos flask.” (a) Open: heat goes in and steam (mass) comes out. (b) Closed: heat and work cross the boundary, but no gas leaves. (c) Isolated, very nearly: neither mass nor heat crosses.
2 marks: “State the zeroth law of thermodynamics. Which quantity does it help to define?” If A and B are each in thermal equilibrium with C, then A and B are in thermal equilibrium with each other. It defines temperature: bodies in thermal equilibrium have the same temperature.
1 marks: “Convert 50 kcal into joules. (1 cal = 4.18 J)” 50 kcal = 50000 cal = 50000 × 4.18 J = 2.09 × 10⁵ J.
Open lets mass and energy through; Closed cuts off mass; Isolated ignores both. Zeroth law: friends of the same friend are friends, at one temperature.