First law of thermodynamics. Gas expansion

In summary, the pressure after expansion of 1.1 kg of air with pressure 10^6 Pa and temperature 125 degrees Celsius, where the volume increases to five times its initial size, can be calculated using the equation dU = 1/4 dW - dW. Since U = 5/2 NKT, we can solve for the end pressure by plugging in the values for start pressure, start volume, and end volume. The resulting pressure is 120000 Pa.
  • #1
Sweden08
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1.1 kg off air with pressure 10^6 Pa, temperature 125 celciusdegrees, gets to expand until the volume is five times bigger than in the beginning. In every moment of the expansion, the amount of (warmth energy = Q) contributed is one fourth of the work done by the gas. 1 kmol of air weighs about 29 kg, Cv=5/2R.
Calculate the pressure after the expansion.



2.
dU = dQ - dW
dU = dQ - pdV
U = 5/2 NKT



3. Since this process is not konstant for either temperature, volume, pressure, i have no clue how to solve it. However:

If dQ = 1/4 dW, then dU = 1/4 dW - dW = -3/4 dW
And since U = 5/2 NKT = 5/2 PV. ---> dU = 5/2 (P1V1-P0V0)

P0= start pressure, V0=start volume, V1= endvolume = 5V0, P1=endpressure=?
 
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  • #2
Plugging in the values we get: -3/4dW = 5/2 (P1V1 - 10^6*V0) -3/4 dW = 5/2 (P1*5V0 - 10^6*V0) -3/4 dW = 5/2 (5P1V0 - 10^6V0) P1 = (3/25)*10^6 = 120000 Pa
 

What is the first law of thermodynamics?

The first law of thermodynamics, also known as the law of conservation of energy, states that energy cannot be created or destroyed, but can only be transferred or converted from one form to another.

What is gas expansion?

Gas expansion is the process by which a gas increases in volume as a result of an increase in temperature or a decrease in pressure. This is due to the fact that gas particles have more kinetic energy at higher temperatures and are able to move further apart, resulting in an increase in volume.

How does the first law of thermodynamics apply to gas expansion?

The first law of thermodynamics states that energy cannot be created or destroyed, but can only be transferred or converted. In the case of gas expansion, the energy of the gas is converted from internal energy (kinetic energy of gas particles) to work as the gas expands against a piston or other system. This conversion of energy is in accordance with the first law of thermodynamics.

What are some real-life examples of gas expansion?

Some real-life examples of gas expansion include a hot air balloon rising due to the expansion of air inside the balloon, the popping of a sealed bag of chips at high altitudes due to the decrease in air pressure, and the release of gas from a can of soda when it is opened, causing the gas to expand and create bubbles.

Can the first law of thermodynamics be violated?

No, the first law of thermodynamics is a fundamental law of physics and cannot be violated. It has been extensively tested and observed to hold true in all physical systems, including gas expansion. Any apparent violation of this law can be attributed to measurement error or incomplete understanding of the system.

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