Problem 19E

What is calorimetry? Explain the difference between a coffeecup calorimeter and a bomb calorimeter. What is each designed to measure?

Solution: The distance between two adjacent crests or troughs is called wavelength. It is denoted by the greek letter lambda() and is generally expressed in terms of Angstrom o o -10 units(A ) [1 A = 10 m] On the other hand, the number of waves which pass through a given point in one second is known as the frequency. It is denoted by the greek letter nu() and is generally expressed in -1 terms of Hertz(Hz) [1 Hz = 1 sec ] If c is the velocity of light, the the relation between wavelength, frequency and velocity of light is given by: c = x ------(1) Step1: -6 -5 -6 a) Given, wavelength of the radiation = 10 m = 10 x 10 m = 10 m [1 m = 10 m] Velocity of light, c = 3 x 10 m/sec 8 Substituting the values in equation (1), we get, 8 -5 frequency() = ( 3 x 10 m/sec) / (10 m) 13 -1 = 3.0 x 10 sec . Thus, frequency of the radiation is 3.0 x 10 sec . 13 -1 Step2: 14 -1 b) Given frequency of the radiation = 5.50 x 10 s . 8 Velocity of light, c = 3 x 10 m/sec Therefore, from equation (1), wavelength() = c/ Substituting the values, we get, = (3 x 10 m/sec) / (5.50 x 10 s ) 14 -1 -6 = 0.545 x 10 m -7 = 5.45 x 10 m -7 Thus, wavelength of the radiation is 5.45 x 10 m. Step3: -7 -7 c) Human eye will respond to wavelengths from about 3.90 x 10 m to 7.0 x 10 m. Thus, radiations in part (b) will be visible to human eye. Step4: d) Distance travelled by the electromagnetic radiation = speed x time 8 Here, speed of the radiation = 3 x 10 m/sec -6 -6 Time travelled = 50 s = 50 x 10 s [1 s = 10 s] 8 -6 Therefore, distance travelled = (3 x 10 m/sec) x (50 x 10 s) = 150 x 10 m. 2 = 1.50 x 10 m. 4 4 Thus, the electromagnetic radiation travels 1.50 x 10 m in 50 s. -----------