Chapter 19: Q. 25 (page 544)

A $65 c m^{3}$ block of iron is removed from an $800^{0} C$ furnace and
immediately dropped into 200 mL of $20^{0}$ C water. What fraction
of the water boils away?

Short Answer

Expert verified

The iron block in this example provided energy to the water until it reached its phase shift. The leftover energy then converted a portion of the water to steam until the system reached equilibrium.

Step by step solution

Given information

Given:

We have $65 {cm}^{3}$ of iron at $800 ° C, 200 mL$ of water at $20 ° C$ .

Formula used:

role="math" localid="1650517403634" $m_{iron} Δ C_{p, iron} Δ T_{i, iron} + m_{water} Δ C_{p, water} Δ T_{i, water} = m_{iron} Δ C_{p, iron} Δ T_{f} + m_{water} Δ C_{p, water} Δ T_{f} + m_{steam} Δ C_{steam}$

Simplification

Let us solve the $m_{steam}$

$m_{iron} Δ C_{p, iron} Δ T_{i, iron} + m_{water} Δ C_{p, water} Δ T_{i, water} - m_{iron} Δ C_{p, iron} Δ T_{f} - m_{water} Δ C_{water} Δ T_{f} = m_{steam} Δ C_{p steam}$

$m_{iron} = 65 [{cm}^{3}] Δ 7.874 [\frac{g}{{cm}^{3}}] = 511.81 [g] m_{water} = 200 [m L] Δ 1 [\frac{g}{m L}] = 200 [g] C_{p, water} = 4.181 [\frac{J}{g Δ K}] C_{p, iron} = 0.450 [\frac{J}{g Δ K}]$

Latent heat to vaporize water:

$C_{steam} = 2257 [\frac{J}{g}] T_{i, water} = 20.0 [{}^{\circ}C] + 273.15 = 293.15 [K] T_{i, iron} = 800 [{}^{\circ}C] + 273.15 = 1073.15 [K] T_{f} = 100.0 [{}^{\circ}C] + 273.15 = 373.15 [K]$

$m_{steam} = \frac{511.81 [g] Δ 0.45 [\frac{J}{g A K}] Δ (1073.15 [K] - 373.15 [K]) + 200 | g | Δ 4.181 [\frac{J}{g A K}] Δ (293.15 [K] - 373.15 [K])}{2257 [\frac{J}{K}]} m_{steam} = 41.79 [g] x = \frac{m_{staia}}{m_{vatir}} = \frac{41.79 ∣ g]}{200 ∣ g]} = 0.209 = 20.9 %$

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A $65 c m^{3}$ block of iron is removed from an $800^{0} C$ furnace and
immediately dropped into 200 mL of $20^{0}$ C water. What fraction
of the water boils away?

Short Answer

Step by step solution

Given information

Simplification

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A 65cm3 block of iron is removed from an8000C furnace andimmediately dropped into 200 mL of 200C water. What fractionof the water boils away?

Short Answer

Step by step solution

Given information

Simplification

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Electricity and Magnetism

Force

Engineering Physics

Linear Momentum

Energy Physics

Fundamentals of Physics

Study anywhere. Anytime. Across all devices.

A $65 c m^{3}$ block of iron is removed from an $800^{0} C$ furnace and
immediately dropped into 200 mL of $20^{0}$ C water. What fraction
of the water boils away?