# Heat energy change when gas compressed

1. Jun 11, 2013

### blueberryfive

1. The problem statement, all variables and given/known data

One mole of an ideal gas is in a container with a moveable piston. A 100 N force moves the piston down 1 m; the compression is isothermal.

Does 100 J of energy leave the gas or enter the gas?

2. Relevant equations

W=Fd
U=Q-W=Q-P(Vf-Vi)

3. The attempt at a solution

W=P(Vf-Vi). Since Vf<Vi, Vf-Vi<0, so W<0. Hence U=Q-W=Q+W. Since the compression is isothermal, U=0, so 0=Q+W <=> Q=-W <=> Q=100 J. So 100 J of heat enters the gas.

2. Jun 11, 2013

### Basic_Physics

Because the change in the internal energy is zero, as you rightly indicate, we know that no netto energy enters or leaves the system. This can also be seen from Q = W. The work done by the pressure of the gas is negative. This means that heat is leaving the system during the compression.

3. Jun 11, 2013

### blueberryfive

Ok, thanks. If the process weren't isothermal, then heat would enter the gas, right?

4. Jun 11, 2013

### Basic_Physics

Not necessarily. We can let heat enter or leave the system by bringing it into contact with a source at a higher or lower temperature, or even isolate it and arrange for an adiabatic compression. Both Q and W signifies energy entering or leaving the system. In this case it enters via W and leaves via Q.

5. Jun 11, 2013

### Staff: Mentor

Actually, both. Heat Q and work W are both considered "energy in transit." So 100 J energy enters by doing work on the gas, and leaves by removing heat from the gas.

Oops. I guess that's the same as Basic_Physics response. Please disregard.

Chet