PHY 182, Spring Semester 2002

Homework #5: Temperature (chapter 21)

Exercise 8:

U(0°C) = 0 mV

U(510°C) = 28.0 mV

è T = (510°C/28.0mV) U

For U = 10.2 mV: T = (510°C/28.0mV) 10.2 mV = 186 °C

Exercise 22:

L_a: length of side a

L_b: length of side b

ΔL_a = α L_a ΔT

ΔL_b = α L_b ΔT

ΔA ≈ ΔL_a * L_b + ΔL_b * L_a = α L_a L_b ΔT + α L_b L_a ΔT = 2 α A ΔT

q.e.d.

Exercise 33:

α(brass) = 1.9 * 10^-5 K^-1 (from Table 21-3, p. 486)

ΔL/L = α*ΔT = 1.9 * 10^-5 K^-1 * 20 K = 3.8*10^-4

Simple Pendulum: period T = 2π(L/g)^1/2

è ΔT/T = ½ ΔL/L = ½*3.8*10^-4 = 1.9*10^-4 = 0.68 s/h

Problem 4:

Δp = 120 mm Hg for ΔT = 100 K

è Δp/ΔT = 120 mm Hg / 100 K

ΔT = (100K/120 mmHg) * Δp

For the unknown temperature: Δp = ± 90 mm Hg (not further specified)

ΔT = (100K/120 mmHg) * (± 90 mm Hg) = ± 75 K

è The temperatures differ by 75 K, i. e. the unknown temperature is 273 K ± 75 K = 198 K or 348 K.