Answer to Question #86774 in Molecular Physics | Thermodynamics for Christian

Question

1. How many joules and kilocalories are generated when the brakes are used to bring a 1300-kg car to rest from a speed of 95 kg/h? (1 cal = 4186 J)

2. An iron boiler of mass 180 kg contains 730 kg of water at 18 *C. A heater supplies energy at the rate of 58,000 kJ/h. How long does it take for the water to:
(a) reach the boiling point,
(b) and all have changed to steam?
(Ciron = 450 J/kg-*C; Cwater = 4186 J/kg-*C; Lv = 2256 kJ/kg)

3. One end of a 56 cm long copper rod with a diameter of 2 cm is kept at 460 *C, and the other is immersed in water 22 *C. Calculate the heat conduction rate along the rod.
(Kcopper = 380 W/m-*C)

Answer 1

1. 

W = ½ mv²

W = ½ x 1300 kg x (26.39 m/s)² = 4.5x10⁵ J

4.5x10⁵ J x 1 kcal / 4186 J = 108 kcal

Answer: 108 kcal

2.

a)

ΔT_w = 100 ^oC – 18 ^oC = 82 ^oC

Q₁ = m_w c_w ΔT_w + m_i c_i ΔT_i ,

ΔT_w = ΔT_i

Q₁ = [(730 x 4180) + (180 x 450)] x 82 = 2.57x10⁸ J

t₁ = Q₁ / P =2.57x10⁸ J / 5.8 x10⁷ J/h = 4.4 h

b.

Q₂ = m L_w = 730 x 22.6x10⁵ = 1.65x10⁹ J

t₂ = Q₂ / P =1.65x10⁹ J / 5.8 x10⁷ J/h = 28 h

t_total = t₁ + t₂ = 4.4 + 28 = 32.4 h

3.

Q = kA (ΔT / L) = 380 x [(3.14 x 0.02²)/4] x (438 / 0.56) = 93.3 W