Thermodynamics problem

In summary: J / (6.75kg x 910 J kg-1 K-1)= 40.5degIn summary, the total heat energy transferred from the water vapour to the plate is 225.82735 kJ, and the change in temperature for the plate is 40.5deg. This means that answer C, 249 kJ, is the correct choice.
  • #1
luysion
35
0

Homework Statement


"100g of water vapour initally at 100deg, condenses on a small aluminium plate. The plate has dimensions 50cmx50cmx1cm and mass 6.75kg. The plate is initially at 5deg, and when thermal equilibium is reached the temperature of plate and water is 45.5deg. The total heat energy transferred to the plate from the water vapour is (in kJ): [The specific heat of aluminium is 910 J kg-1 K-1 the specific heat of water is 4190 J kg-1 K-1 and the latent heat of vapourisation for water is 2256 kJ kg-1]"

Homework Equations





The Attempt at a Solution



Hey, I am really confused as to what to do with this thermodynamics problem, like I know I can calculate Q1 to find the heat given from the water to the plate, but I am not sure about what to do about latent heat and the volume. The possible answers are
A)173
B)205
C)249
D)281
E)311

could somone please show me the working out I have an exam tomorrow and I can't contact my lecturers (they won't reply lol)

cheers guys
 
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  • #2


Hi there,

First, we need to calculate the mass of water vapour that has condensed on the plate. We know that the initial mass of water vapour was 100g, and since it has all condensed onto the plate, the final mass of water on the plate is also 100g.

Next, we need to calculate the heat energy transferred from the water vapour to the plate. We can do this using the equation Q = m x c x ΔT, 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 water vapour, we have:

Q1 = 100g x 4190 J kg-1 K-1 x (100deg - 45.5deg)
= 100g x 4190 J kg-1 K-1 x 54.5deg
= 227350 J

Next, we need to consider the latent heat of vapourisation for water. This is the amount of heat energy required to change 1kg of water from liquid to gas at its boiling point. Since we have 100g of water, we need to calculate the latent heat for 0.1kg of water:

Q2 = 0.1kg x 2256 kJ kg-1
= 225.6 kJ

Now, we can calculate the total heat energy transferred from the water vapour to the plate:

Qtotal = Q1 + Q2
= 227350 J + 225.6 kJ
= 225.82735 kJ

Finally, we need to calculate the change in temperature for the plate. We can use the equation Q = m x c x ΔT, 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 plate, we have:

Q = 6.75kg x 910 J kg-1 K-1 x (45.5deg - 5deg)
= 6.75kg x 910 J kg-1 K-1 x 40.5deg
= 246862.5 J

Now, we can use this value to calculate the change in temperature for the plate:

246862.5 J = 6.75kg x 910 J kg-1 K-1 x ΔT
ΔT =
 

What is thermodynamics?

Thermodynamics is the branch of physics that deals with the relationships between heat, energy, and work.

What is a thermodynamics problem?

A thermodynamics problem is a question or scenario that involves the principles and laws of thermodynamics to solve for unknown variables or to analyze a system's behavior.

What are the laws of thermodynamics?

The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or converted from one form to another. The second law states that the total entropy of a closed system will never decrease over time, and the third law states that the entropy of a pure crystalline substance at absolute zero temperature is equal to zero.

What is the difference between heat and temperature in thermodynamics?

Heat is the transfer of energy from a warmer object to a cooler object, while temperature is a measure of the average kinetic energy of the particles in a substance. In thermodynamics, heat is often used to increase the temperature of a system.

How do you solve a thermodynamics problem?

To solve a thermodynamics problem, you need to identify the known and unknown variables, choose an appropriate thermodynamic law or equation to use, and then apply the appropriate formulas to solve for the unknown variables. It is important to pay attention to units and correctly apply the laws of thermodynamics to arrive at the correct solution.

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