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Old May 25th 2017, 06:35 AM   #1
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A-Level ideal gas law problem?

A fixed mass of nitrogen gas is originally held in a 2 dm^3 volume container at a pressure of 101 kPa and a temperature 15 degrees celsius.

The gas is compressed slowly within the container under isothermal conditions until it reaches a new volume of 1 dm^3.

It is then heated at a constant volume, absorbing 162 J of heat.
The gas is then allowed to expand rapidly in an adiabatic process until it reaches its original pressure and volume.

Calculate the pressure and temperature of the nitrogen gas at the start of its adiabatic expansion (y for nitrogen is 1.4)

Method would be much appreciated. Thank you
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Old May 26th 2017, 04:28 AM   #2
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The "ideal gas law" is PV= NRT where P is the pressure, V the volume, N the number of molecules in the gas, R is "Avogadro's number", [tex]6.02 x 10^{23}[/tex], and T is the temperature in degrees Kelvin. To begin, P is 101 kPa, V is 2 dm^3, and T is 15 degrees Celsius= 288.15 degrees Kelvin. From those, you can calculate N for this situation.

"The gas is compressed slowly within the container under isothermal conditions until it reaches a new volume of 1 dm^3."

"isothermal" means that T does not change. N, R, and T while V is now 1 dm^3 rather than 2 dm^3. Since the right side, "NRT" does not change while V is halved, P must double to 202 kPa.

"It is then heated at a constant volume, absorbing 162 J of heat. "
Adding 162 J of heat will increase the temperature, T, by how many degrees?
(The specific heat of Nitrogen is approximately 1.4 Kilo-Joules per kilogram per degree Kelvin.)
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