Some gas is trapped in a large syringe by a piston.The atmospheric pressure is 100kpa.The pressure gauge indicates that the gas pressurr is 200kpa above atmospheric pressure.The piston moves outwards and the volume of the gas doubles.The temperature remains constant.What is the new gas pressure?

The new gas pressure is 150 kPa.

Explanation :

Boyle's Law: This law states that pressure is inversely proportional to the volume of the gas at constant temperature and number of moles.

    (At constant temperature and number of moles)

where,

= initial pressure of gas  = (100+200) kPa = 300 kPa

= final pressure of gas  = ?

= initial volume of gas  = v

= final volume of gas  = 2v

Therefore, the new gas pressure is 150 kPa.

Since the system itself is giving off heat, this is a reduction in the internal energy.

heat = - 25,000 J

Since work is being done on the system, therefore it is an additional energy to the system. Work is given as:

work = - P dV

work = - 1.50 atm (6 L – 12 L)

work = 9 L atm

Since it is given that 1 L atm is equivalent to 101.3 J, therefore the total energy added is:

energy due to work = 9 L atm (101.3 J / 1 L atm)

energy due to work = 911.7 J

Therefore the total change in internal energy is the sum of heat and energy due to work:

Change in internal energy = - 25,000 J + 911.7 J

Change in internal energy = - 24,088.3 J

Therefore, approximately 24.1 kJ of energy is lost by the system in the total process.

-24.1 kJ