212k views
5 votes
Heat capacity of ice: 2090 J kg-1 °C-1 Heat capacity of water (liquid): 4186 J kg-1 °C-1 Latent heat of fusion: 3.36×105 J kg-1 Latent heat of vaporization: 2.26×107 J kg -1 Give your answers to at least three significant figures. Your answers must be accurate to 1%. How much heat energy is required to raise the temperature of 220 g of ice from a temperature of -43 °C to a temperature of -22 °C? J Tries 0/10

How much heat energy is required to raise the temperature of 220 g of water from a temperature of 48 °C to a temperature of 54 °C? J
How much heat energy is required to raise the temperature of 220 g of water (initially ice) from a temperature of -43 °C to a temperature of 54 °C? J Tries 0/10
How much heat energy is required to evaporate 220 g of water which is initially at a temperature of 48 °C? J Tries 0/10

User Mwilson
by
7.7k points

1 Answer

1 vote

Final answer:

The heat energy required for temperature changes and phase transitions is calculated using the specific heat capacities and latent heats. Results show significant energy required, particularly for phase changes involving melting and vaporization.

Step-by-step explanation:

To calculate the heat energy required for the temperature changes and phase transitions described in the student's question, we use the formula Q = mcΔT where Q is the heat energy, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.

For the first part of the question, raising the temperature of 220g of ice from -43°C to -22°C only requires calculating the energy for the increase in temperature as no phase change occurs. Thus:

Q = mcΔT
= (0.220 kg)(2090 J/kg°C)(-22°C - (-43°C))
= 0.220 kg * 2090 J/kg°C * 21°C
= 9614.6 J

For the second part, raising the temperature of 220 g of water from 48°C to 54°C without a phase change involves:

Q = mcΔT
= (0.220 kg)(4186 J/kg°C)(54°C - 48°C)
= 0.220 kg * 4186 J/kg°C * 6°C
= 5534.32 J

The third part, which includes heating the ice to water, then to 54°C, requires multiple steps that include heating the ice, melting it (using latent heat of fusion), and then heating the resultant water. The fourth part involving the evaporation of water at 48°C also requires multiple steps, and the large amount of energy is due to the latent heat of vaporization.

User Steven Ogwal
by
8.0k points