CBSE Class 10 Physics Heat Notes Set 08

Thermal Conductivity

When the ends of a uniform rod are kept at steady temperatures θ₁ and θ₂ (θ₁ > θ₂), heat flows along the rod and the temperature falls steadily, so there is a temperature gradient (θ₁ − θ₂)/d. The heat Q conducted is proportional to the area A, the temperature difference and the time t, and inversely proportional to the length d:

Q = K A (θ₁ − θ₂) t / d

K is the coefficient of thermal conductivity: the heat that flows per second through unit area for unit temperature gradient. Its SI unit is W m^-1 °C^-1 (CGS: cal s^-1 cm^-1 °C^-1). Metals are good conductors (silver best, then copper, aluminium and iron); liquids other than mercury, gases, wood and cork are poor conductors.

To compare metals, rods of the same size are soldered to a copper vessel, coated with wax and heated by steam. The wax melts up to some distance l on each rod, and K is proportional to l² . Example: heat 80 W is supplied to a copper rod of area 10 cm² and length 20 cm with ends at 90 °C and 50 °C: K = 80 × 0.2 / (10 × 10^-4 × 40) = 400 W/m °C.

Example. A glass vessel of area 100 cm² and thickness 1.5 mm holds ice at 0 °C and is surrounded by steam at 100 °C. Heat per minute = 0.777 × 0.01 × 100 × 60 / 0.0015 = 31 080 J. Ice melted = 31 080 / 336 000 = 92.5 g. For two rods in series the heat flow through both is the same.

Thermocouple and Thermopile

If two dissimilar metals (copper and iron, antimony and bismuth, platinum and rhodium) are joined at their ends to form a closed circuit and the two junctions are kept at different temperatures, an emf is produced and a current flows through a sensitive galvanometer. This is the Seebeck effect. The emf grows with the temperature difference of the junctions, so the device can be calibrated to measure temperature.

Several thermocouples joined in series form a thermopile. All the cold junctions are on one side and the hot ones on the other, coated with lamp black so that they absorb radiation. A larger galvanometer current means more intense heat radiation, so the thermopile measures thermal radiation.

Heat Radiation

Heat radiation travels in straight lines at the speed of light, 3 × 10⁸ m/s, as an electromagnetic wave. It is reflected and refracted like light, and its intensity falls as the inverse square of the distance from the source. Black surfaces are better absorbers and better emitters tha polished ones: a good absorber is a good emitter.

Refrigeration

In a heat engine heat is taken in at a high temperature, part becomes work and the rest is rejected at a lower temperature. A refrigerator does the opposite: using work from a compressor, it takes heat from the cold space and discharges more heat at the higher temperature. A gas such as ammonia or Freon is liquefied by compression and then evaporates in the freezer, taking latent heat from the inside, after which the vapour returns to the compressor. These gases can be liquefied by pressure alone because their critical temperatures are above room temperature, and their latent heats are high.

Atmospheric Moisture, Dew Point and Relative Humidity

Air holds water vapour, and warm air can hold more than cool air. Air containing the most it can hold at a temperature is saturated. If unsaturated air is cooled to a certain temperature it becomes saturated and dew forms; this temperature is the dew point.

Relative humidity (R.H.) = saturated vapour pressure at the dew point / saturated vapour pressure at the air temperature. Example: air at 30 °C with dew point 10 °C: R.H. = 9.21 / 31.84 = 28.9%.

To find the dew point, a polished aluminium cup holding water is cooled by adding ice while stirring. The temperature at which the outside just becomes dim with moisture is noted, and again the temperature at which the dimness just disappears on warming; the average is the dew point. A wet and dry bulb hygrometer has two thermometers, one with its bulb wrapped in wet muslin. Evaporation cools the wet bulb, so it reads lower; a large difference means dry air (low R.H.), and no difference means R.H. = 100%.