First law of thermodynamics: why some equations can't be used

In summary, the problem involves a cylinder with an ideal gas at a certain pressure and temperature. The gas is then heated at constant pressure and cooled at constant volume, with a heat extraction of 63J. To calculate the total heat input in stage (i), we first need to determine the work done by the gas, which is 25J. Then, using the equation U=(3/2)pV, we can find the change in internal energy (ΔU) for stage (i). However, this approach is incorrect and instead, we need to use the total change in internal energy from stage (i) to (ii) to calculate the heat input. The reason for this is that the equation U=(3/2
  • #1
ashash_ash
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Homework Statement


A cylinder fitted with a frictionless piston contains 5.0×10-4m3 of an ideal gas at a pressure of 1.0×105 Pa and temperature of 300K.
The gas is then
(i) heated at constant pressure to 450K, and then
(ii) cooled at constant volume to the original temperature of 300K. The heat extracted in this stage is 63J.

Calculate the total heat input in stage (i)

2. The attempt at a solution
Ok, so firstly, I determined the work done by the gas in stage (i), which is 25J. (this is the correct answer)
After, as we know that internal energy of an ideal gas U = (3/2)PV, I thought I could find the change in internal energy ΔU of stage (i) by using ΔU=(3/2)pΔV, then use the first law of thermodynamics ΔU=Q+W to determine the heat input. However, my answer was wrong. :nb)

Apparently you can't do that. And instead, the answer key made use of the total change in internal energy from stage (i) to (ii) instead. However, I am really confused, as now I am unsure of when exactly I should or should not make use of the equation U=(3/2)pV

Would really appreciate some help! Thank you!:smile:
 
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  • #2
That's only for monatomic ideal gases. Do you know how U varies with T for molecules with degrees of freedom other than translation? You don't actually need to know this; you can get Cv from part (ii), work out Cp and use it in part (i).
 
  • #3
From the problem statement, how many moles of gas do you have?
 

1. What is the first law of thermodynamics?

The first law of thermodynamics is a fundamental principle in thermodynamics that states that energy cannot be created or destroyed, only transferred or converted from one form to another.

2. Why can't some equations be used when applying the first law of thermodynamics?

Some equations cannot be used when applying the first law of thermodynamics because they may not accurately account for all forms of energy transfer or conversion, or they may not take into account the specific conditions of the system being studied.

3. How do you know which equations can be used when applying the first law of thermodynamics?

To determine which equations can be used when applying the first law of thermodynamics, you must carefully consider the specific conditions and variables of the system, and choose equations that accurately account for all forms of energy transfer and conversion within that system.

4. Can the first law of thermodynamics be violated?

No, the first law of thermodynamics is a fundamental law of physics and cannot be violated. The total amount of energy in a closed system will always remain constant, even if it is transferred or converted into different forms.

5. How does the first law of thermodynamics relate to the conservation of energy?

The first law of thermodynamics is essentially a statement of the principle of conservation of energy. It states that energy cannot be created or destroyed, only transformed from one form to another. This is consistent with the principle of conservation of energy, which states that the total energy in a closed system is always constant.

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