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# Energy and work done by a gas system

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An insulated cylinder closed at one end by a frictionless piston contains 20g of hydrogen gas at 30 degrees Celsius. This is heated to 40 degrees Celsius with the pressure kept constant at 1 bar and the volume increases by 7*10^-4 m^3. (The specific heat of H2 at constant pressure is 1.4*10^4 JKg^-1 K^-1).

a) What is the work done by the gas?

b) What is the change in internal energy of the system?

https://brainmass.com/physics/internal-energy/energy-work-done-gas-system-182058

## SOLUTION This solution is FREE courtesy of BrainMass!

Work done by a system is defined as:

And the total work of a system starting at volume Vi and ends up with volume Vf is:

In most cases, the pressure and volume are interlinked (the pressure is a function of the volume). However, in this case the pressure is constant (isobaric process).

Thus, in the integral expression for work the pressure can be taken outside of the integral:

In our case the work done by the system is:

So the system spent 70 joules of work (the volume increased).

The heat change is defined as:

Where:

• M is the mass of the gas
• c is the specific heat capacity
• T is the change in temperature

Note that since we are dealing with the difference between the final and initial temperatures, the difference is the same in Kelvin units as in Celsius units.

In this case:

The first law of thermodynamics is simply energy conservation law:

It says that the change in the internal energy of the gas E (which is the internal reservoir of energy in the system) is the difference between the heat energy Q that flowed into the system (the system gains energy) and the work that was done by the system (the system loses energy).

When heat flows out of the system the sign of Q is negative and when work is done on the system (e.g. compression) the work value is also negative.

In our case we gained 2800J from the heating of the gas and we (the system) spent 70J to expand, hence the change in internal energy is:

The system internal energy has increased by 2730J

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