THERMAL PROPERTIES OF MATTER

skin temperature may be ° ° C (say). The emissivity of the skin is about . for the relevant region of electromagnetic radiation. The rate of heat loss is: H = . × – × . × . × {( ) – ( ) } = . W which is more than half the rate of energy production by the body at rest ( W). To prevent this heat loss effectively (better than ordinary clothing), modern arctic clothing has an additional thin shiny metallic layer next to the skin, which reflects the body’s radiation. . NEWTON’S LAW OF COOLING We all know that hot water or milk when left on a table begins to cool, gradually. Ultimately it attains the temperature of the surroundings. To study how slow or fast a given body can cool on exchanging heat with its surroundings, let us perform the following activity. Take some water, say mL, in a calorimeter with a stirrer and cover it with a two-holed lid. Fix the stirrer through one hole and fix a thermometer through another hole in the lid and make sure that the bulb of thermometer is immersed in the water. Note the reading of the thermometer. This reading T is the temperature of the surroundings. Heat the water kept in the calorimeter till it attains a temperature, say ° C above room temperature (i.e., temperature of the surroundings). Then, stop heating the water by removing the heat source. Start the stop-watch and note the reading of the thermometer after a fixed interval of time, say after every one minute of stirring gently with the stirrer. Continue to note the temperature ( T ) of water till it attains a temperature about ° C above that of the surroundings. Then, plot a graph by taking each value of temperature ∆ T = T – T along y-axis and the coresponding value of t along x-axis (Fig. . ). Fig. . Curve showing cooling of hot water with time. From the graph you can infer how the cooling of hot water depends on the difference of its temperature from that of the surroundings. You will also notice that initially the rate of cooling is higher and decreases as the temperature of the body falls. The above activity shows that a hot body loses heat to its surroundings in the form of heat radiation. The rate of loss of heat depends on the difference in temperature between the body and its surroundings. Newton was the first to study, in a systematic manner, the relation between the heat lost by a body in a given enclosure and its temperature. According to Newton’s law of cooling, the rate of loss of heat, – d Q /d t of the body is directly proportional to the difference of temperature ∆ T = ( T –T ) of the body and the surroundings. The law holds good only for small difference of temperature. Also, the loss of heat by radiation depends upon the nature of the surface of the body and the area of the exposed surface. We can write ( . ) where k is a positive constant depending upon the area and nature of the surface of the body. Suppose a body of mass m and specific heat capacity s is at temperature T . Let T be the temperature of the surroundings. If the temperature falls by a small amount d T in time d t , then the amount of heat lost is d Q = ms d T