Solving Heat Problems: 2 Questions & Exam Tomorrow

[shemer77]

Hi, I have 2 questions and an exam tomorrow, and I have no idea how my teacher answered these 2 problems, if someone can guide me through how to solve these problems i would really appreciate it. I am not looking for an answer just a step by step how to solve it and I am not really sure how to start.

How much heat is lost in one day through the roof of a 5.00m by 5.00m room?The room is maintained at a temperature of 20°C but the outdoor temperature is only -4°C.

How much heat, Q, is required to convert 0.500kg of ice at -30.0°C to steam at 140.0°C

For this one, i think my teacher would convert the ice to a liquid and then to a solid, and then taking taking some equation at each part, lol I am not really sure

thanks in advance :)

 

[PeterO]

Hi, I have 2 questions and an exam tomorrow, and I have no idea how my teacher answered these 2 problems, if someone can guide me through how to solve these problems i would really appreciate it. I am not looking for an answer just a step by step how to solve it and I am not really sure how to start.

For this one, i think my teacher would convert the ice to a liquid and then to a solid, and then taking taking some equation at each part, lol I am not really sure thanks in advance :)

For the roof, I think you need to know the thermal resistance or thermal conductivity of the material of the roof. With that you can calculate the heat flow per square meter [Joules per sec per square meter] then scale it up for the room size and the time period.

For the ice to steam.

Heat the ice - what is the specific heat for ice? [it is 1 for water]
melt the ice - what is the latent heat for melting ice?
Heat the water
evaportate the water - what is the latent heat of evaportation?
heat the steam - what is the specific heat for steam?

NOTE: Suppose the latent heat for melting ice was 50 times the specific heat for water -it's NOT - the getting from ice at -10 to water at +10 would be the same as heating water from +5 to +75, ie 70 degrees.

You could convert each section to a "heating water" equivalent and do the final calculation in one go.

***Saying latent heat is 50 times specific heat I mean suppose you need X Joules to heat a mass of water by 1 degree but need 50X Joules to melt the same mass of ice.

 

[shemer77]

For the roof, I think you need to know the thermal resistance or thermal conductivity of the material of the roof. With that you can calculate the heat flow per square meter [Joules per sec per square meter] then scale it up for the room size and the time period.

For the ice to steam.

Heat the ice - what is the specific heat for ice? [it is 1 for water]
melt the ice - what is the latent heat for melting ice?
Heat the water
evaportate the water - what is the latent heat of evaportation?
heat the steam - what is the specific heat for steam?

NOTE: Suppose the latent heat for melting ice was 50 times the specific heat for water -it's NOT - the getting from ice at -10 to water at +10 would be the same as heating water from +5 to +75, ie 70 degrees.

You could convert each section to a "heating water" equivalent and do the final calculation in one go.

***Saying latent heat is 50 times specific heat I mean suppose you need X Joules to heat a mass of water by 1 degree but need 50X Joules to melt the same mass of ice.

sorry, i didnt really learn this stuff. How would I go about calculating the heat flow?

and for the ice to steam, what do you mean by convert each section to a heating water equivalent?

 

[PeterO]

sorry, i didnt really learn this stuff. How would I go about calculating the heat flow?

and for the ice to steam, what do you mean by convert each section to a heating water equivalent?

If you don't immediately understand the conversions, ignore them and work it out the "standard" way.

There is a conductance [or its inverse resistance] which tells you the number of joules per second per square metre per degree difference each side. You need to cram that stuff now.

[You may have seen ceiling insulation bats. They can be R2, R3, R4 etc bats - that is referring to their thermal resistance.

 

[rwisz]

Hello,

Thank you for reaching out for help with your heat problems. I am happy to guide you through the process of solving these questions.

For the first question, we need to use the equation Q = mCΔT, where Q represents the amount of heat, m is the mass of the material, C is the specific heat capacity, and ΔT is the change in temperature. In this case, we are looking for the amount of heat lost, so we will use a negative value for Q.

First, we need to calculate the mass of the air in the room. Since the room is 5.00m by 5.00m, the area is 25m². Assuming the height of the room is 3m, the volume of air in the room is 25m² x 3m = 75m³. Air has a density of approximately 1.2 kg/m³, so the mass of air in the room is 75m³ x 1.2 kg/m³ = 90kg.

Next, we need to calculate the change in temperature. We know that the room is maintained at 20°C, and the outdoor temperature is -4°C. Therefore, the change in temperature is 20°C - (-4°C) = 24°C.

Now, we need to find the specific heat capacity of air. This value varies depending on the temperature and pressure, but for simplicity, we will use an average value of 1005 J/kg°C.

Putting all of this information into the equation, we get Q = 90kg x 1005 J/kg°C x (-24°C) = -2,160,000 J. This means that the room loses 2,160,000 joules of heat in one day through its roof.

For the second question, we need to use the equation Q = mL, where Q represents the amount of heat, m is the mass of the material, and L is the latent heat of fusion or vaporization. In this case, we are converting ice to steam, so we will use the latent heat of vaporization, which is 2,260,000 J/kg.

First, we need to calculate the mass of the ice. We are given that the mass is 0.500kg.

Next, we need to calculate the change in temperature. The ice is at -30.0°C, and we want to convert