1.How many Joules of”heat are given out when a piece ofiron of”mass 50 g and specific v’fieat capacity 460 J/kg K, cools front 80 C to 20 C? To say that the specific heat capacity of iron is 460 J/kg K means that 1 kg of iron gives out or takes in, as the case may be, 460 J when its temperature changes by 1 K. It follows that 50 g (= 0.05 kg) of iron in cooling through 1 K gives out,
so that ((}2 – (}d = change in temperature in kelvins. N ate. The Greek letter () (theta) is the accepted symbol for temperature in “C, If t is used instead of () it may lead to confusion in equations where t is used to represent time in seconds.
2. What is the final temperature of the mixture if” 100 g of”water at 70 DC is added to v 200 g of cold water at 10 “C and well stirred? (Neglect heat absorbed by the container.i From the table above we note that the spec~ificA,.heat capacity of water is 4200 J/kg K. -, _ , _ () .7 ,,0 ‘ Heat given out by hot water = heat received by cold water. Let the final temperature of the mixture = ()in °C Then, change in temperature of hot water = (70 – ()) in kelvins and, change in temperature of cold water = (()- 10) in kelvins Thus, using the formula mC((}2 – (}l) explained in the previous example, we substitute values in the equation. Heat given out by hot water = heat received by cold water which gives (remembering to convert g to kg), 0.1 x 4200 x (70 – ()) = 0.2 x 4200 x (() – 10)
3. The temperature of a piece of copper of mass 250 g is raised to 100°C and it is then transferred to a well-lagged aluminium can of mass 10.0 g containing 120 g of mentholated spirit at 10.0 “C. Calculate the final steady temperature after the spirit has been well stirred. Neglect the heat capacity of the stirrer and any losses from evaporation and use the table of specific heat capacities on age 199 for any data required.
4. The temperature of 500 g of a certain metal is raised to 100°C and it is then placed in 200 gof water at 15°C. If the final steady temperature rises to 21°C, calculate the specific heat capacity of the metal.