Question

A 2.0 kg bar of copper is heated at atmospheric pressure so that its temperature increases from 20°C to 50°C. (a) What is the work done on the copper bar by the surrounding atmosphere? SOLUTION Conceptualize This example involves a solid, whereas the preceding two examples involved liquids and gases. For a solid, the change in volume due to thermal expansion is very small. Categorize Because the expanslon takes place at constant atmospheric pressure, we categorize the process as isobaric Analyze Find the work done on the copper bar using WV) у» Express the change in volume using Δν ν ΔΤ and that Use the following as nece55ary; α, p , and ΔΤ. Do not substitute numerical values, use variables only. ; Substitute for the volume in terms of the mass and density of the copper (Usethe following as necessary: m and p. Do not substitute numerical values; use varlables only.) AT Substitute numerical values. The average linear expansion coefficient for copper is given in the Table of Average Expansion Coefficients. The density of copper is given in the Table of Densities. (Enter your answer in J.) Because this work is negative, work is done -Select- How much energy (in J) is transferred to the copper bar by heat? SOLUTION Use the following equation and the specific heat of copper from the Table of Specific Heats (b) (c) What is the increase in internal energy (in J) of the copper bar? SOLUTION Use the first law of thermodynamics:

Answer 1

(a) W = -P Delta T W = -P (beta v_i Delta T) W = -3 P alpha v_i Delta T W = -3 alpha P (m/rho) Delta T W = -3 times 1.7 times 10^-5 times 101325 times (2 kg/8920 kg/m^3) (30 degree C) W = -0.03476 J (b) Q = mc Delta T = (2 kg) (387 J/kg degree C) times 30 degree C = 23220 J (c) Delta E_int = Q + W = 23219.966 J Exercise -0.27 = -3 times alpha times 101325 (2/rho) (50 degree C) alpha/rho = 8.88 times 10^-9 For Al, alpha = 2.3 times 10^-5 rho = 2700 For Brass, alpha/rho = 2.17 times 10^-9 alpha/rho = 8.6 times 10^-9 Aluminum