Friday, January 22, 2010

Temperature and heat

Temperature and heat

Question 1

The Eiffel Tower, constructed in 1889 by Alexandre Eiffel, is an impressive latticework structure made of iron. If the tower is 301m high on a 22⁰C day, how much does height decrease when the temperature cools to 0.0⁰C?

Solution

∆L = αL0∆T

= (12 × 10⁻⁶ k⁻¹)(301 m)(-22K)

= -7.9cm

Question 2

The heat capacity of 1.00kg of water is 4186J/K.what is the temperature change of the water if(a)505 J of heat is added to the system, or (b)1010 J of heat is removed?

Solution

∆T = Q/C

= 505J/(4186J/K)

= 0.121K

∆T = Q/C

= -1010J/(4186J/K)

= 0.121K

Question 3

Calculate the radiated power from a sphere with a radius of 5.00 cm at the temperature 355 K. Assume the emissivity is unity.

Solution

P = eσ AT⁴

= (1)[5.67 × 10⁻⁸W/(m²·K⁴)]4π(0.0500m)²(355k)⁴

= 28.3W

Question 4

On New Year’s Day several human “polar bears” prepare for their annual dip into the icy waters of Narragansett Bay. One of these hardy soyls has a surface area of 1.15m² and a surface temperature of 303 K( -30⁰C). Find the net radiated power from this person (a) in a dressing room , where the temperatura is 293K(-20⁰C), and (b) outside, where the temperature is 273K (-0⁰C). Assume an emissivity of 0.900 for the person’s skin.

Solution

Pnet = eσ(T⁴-Ts⁴)

= (0.900)[5.67×10⁻⁸W/(m²·K⁴)](1.15m²)×[(303K)⁴ - (293K)⁴]

= 62.1W

Pnet = eσ(T⁴-Ts⁴)

= (0.900)[5.67×10⁻⁸W/(m²·K⁴)](1.15m²)×[(303K)⁴ - (273K)⁴]

= 169W

Question 5

(a) Suppose the volume V in Fig,15-7 is 30.0ml, while taht of V is 200 ml. What fraction, x, of the mass of the liquid has vaporized(at pressure P) when the volume is V = 100mL?

(b) If the heat of vaporization of this fictitious substance is 600kJ/kg and the mass is 80 g, how much heat must be added to the 30.0mL of liquid to reach the volume 100mL?

Solution

V = 100mL

= (1-x)(30.0mL)+x(200mL)

= 0.41

Amount of liquid is (0.41)(80 g) = 32.8g

= heat = (600kJ/kg)(0.0328 kg)=19.7kJ

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