How many BTUs are required to convert 1 pound of ice at 20°F to steam at 220°F?

• A. Approximately 970 BTU
• B. Approximately 2,000 BTU
• C. Approximately 1,320 BTU
• D. Approximately 800 BTU

Answer: (C)

Verified step by step guidance

1. Identify the different stages involved in converting 1 pound of ice at 20°F to steam at 220°F. These stages are: heating the ice from 20°F to 32°F, melting the ice at 32°F to water, heating the water from 32°F to 212°F, vaporizing the water at 212°F to steam, and finally heating the steam from 212°F to 220°F.
2. Calculate the heat required to raise the temperature of ice from 20°F to 32°F using the formula \(q = m \times C_{ice} \times \Delta T\), where \(m\) is the mass (1 lb), \(C_{ice}\) is the specific heat capacity of ice (approximately 0.5 BTU/lb°F), and \(\Delta T\) is the temperature change (32 - 20 = 12°F).
3. Calculate the heat required to melt the ice at 32°F using the heat of fusion: \(q = m \times \Delta H_{fusion}\), where \(\Delta H_{fusion}\) for water is approximately 144 BTU/lb.
4. Calculate the heat required to raise the temperature of water from 32°F to 212°F using \(q = m \times C_{water} \times \Delta T\), where \(C_{water}\) is the specific heat capacity of water (approximately 1 BTU/lb°F) and \(\Delta T\) is (212 - 32 = 180°F).
5. Calculate the heat required to vaporize the water at 212°F using the heat of vaporization: \(q = m \times \Delta H_{vaporization}\), where \(\Delta H_{vaporization}\) is approximately 970 BTU/lb. Then calculate the heat required to raise the steam temperature from 212°F to 220°F using \(q = m \times C_{steam} \times \Delta T\), where \(C_{steam}\) is approximately 0.48 BTU/lb°F and \(\Delta T\) is (220 - 212 = 8°F). Finally, sum all these heat quantities to find the total BTUs required.