#498 A piston-cylinder device contains 2.2 kg of nitrogen

A piston-cylinder device contains 2.2 kg of nitrogen - Mechanical Engineering

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Free Chegg Question

A piston-cylinder device contains 2.2 kg of nitrogen initially at 100 kPa and 25°C. The nitrogen is now compressed slowly in a polytropic process during which constant until the volume is reduced by one-half. Determine the work is done and the heat transfer for this process.

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Free Chegg Answer

1. Step 1 of 7

   Express the energy balance equation for closed system.

   

   Here, energy transfer in to the system is , energy transfer from the system is  and change in internal energy of system is .

   Substitute  for ,  for  and  for .

    ……. (1)

   Here, boundary work done input is , amount of heat transfer exit from the system is  and change in internal energy is .

   Substitute  for  in Equation (1).

    ……. (2)

   Here, mass of system is m, specific heat at constant volume is , initial temperature is  and final temperature is .

2. Step 2 of 7

   Calculate the final pressure  of nitrogen gas inside the cylinder.

   

   Here, initial pressure is  and initial volume is  and final volume is .

   Consider the volume is reduced by one half due to compress of nitrogen gas in polytrophic process.

   Substitute, 2 for  and  for .

   

3. Step 3 of 7

   Calculate the final temperature  of oxygen in the tank.

   

   Here, initial temperature is , final temperature is  and initial pressure is .

   Convert the unit of initial temperature from degree Celsius to Kelvin.

   

   Substitute  for ,  for , 2 for  and  for .

   

4. Step 4 of 7

   Express the boundary work done input for polytrophic process.

   

   Here, pressure inside the cylinder is P.

   Integrate the above equation.

    ……. (3)

   Here, the polytrophic constant is n, the initial volume of piston-cylinder is , the final volume of piston-cylinder is , the initial pressure inside the cylinder is  and final pressure inside the cylinder is .

5. Step 5 of 7

   Substitute    for   and  for  in Equation (3).

   

   Here, the mass of nitrogen gas inside the cylinder is m, the gas constant is R, initial temperature is  and final temperature is.

   From the gas constant properties table, select the gas constant of nitrogen as .

    

6. Step 6 of 7

   Substitute 1.3 for n,  for R,  for m,  for  and  for .

    

   

   Hence, the boundary work done input for the polytrophic process is .

7. Step 7 of 7

   Calculate the amount of heat transfer  exit from the cylinder.

   

   From the ideal gas specific heats of various common gases table, select the specific heat at constant volume of nitrogen at temperature of 300 K as .

   Substitute  for m,  for ,  for ,  for  and  for .

   

   Hence, the amount of heat transfer exit from the cylinder is .