Engine Cycle Homework: Energy Transfer & Exhaust Heat Questions

[GBA13]

Homework Statement

Hi Guys,

I did a heat engine experiment where we put a weight on a piston and moved an air cylinder in a hot water bath, then removed the weight and but the air cylinder in a cold water bath to make a heat engine cycle.

I am just wondering in the simple heat engine which would be larger, The energy transfer from heat reservoir to gas (which I think is the same as the PdV work) or the mechanical work which happens as the piston (with a weight on top) in raised.

I'm also wondering when in an engine cycle is the heat being exhausted to the atmosphere rather than to the cold reservoir?

Homework Equations

The Attempt at a Solution

I think they would actually be the same size. As it is a full cycle then internal energy = 0 so Q14 = W14.

Any help would be appreciated!

Thanks,

Mark

 

[rude man]

Homework Statement

Hi Guys,

I did a heat engine experiment where we put a weight on a piston and moved an air cylinder in a hot water bath, then removed the weight and but the air cylinder in a cold water bath to make a heat engine cycle.

I am just wondering in the simple heat engine which would be larger, The energy transfer from heat reservoir to gas (which I think is the same as the PdV work) or the mechanical work which happens as the piston (with a weight on top) in raised.

In this part of the cycle the heat transferred is greater than the work performed, since the internal energy of the gas has to be raised in temperature as the piston rises.

I'm also wondering when in an engine cycle is the heat being exhausted to the atmosphere rather than to the cold reservoir?

The atmosphere is the cold reservoir (in an auto engine for example).

The first law of thermodynamics states that the change in internal energy of the system (the gas here) = the heat transferred from 'outside' to the system minus the net work done by the system. This is true for any part of the cycle, even an infinitesimally small part: dU = δQ - δW = δQ - pdV.

The net work per cycle is the work done by the system as your piston rises minus the work done on the system as the piston falls.
The net heat transferred per cycle is the heat absorbed by the system while the piston is rising minus the heat lost by the system as the piston falls. And, you state correctly that W₁₄ = Q₁₄. Except yours is a 2 cycle engine so I guess the subscripts should be 12.

 

[Mark44]

I'll take a shot at this (I could be wrong, though). Your explanation was a bit unclear. I think what you were saying is that you put a weight on the piston, and then moved the cylinder and piston to a warm bath. This causes the piston to raise the weight. After that, you put the cylinder and piston in cold water, which caused the piston to retract to a lower position.

The heat transfer would be greater than the change in potential energy, because some of the energy is lost due to friction and other effects (such as heat lost through conduction). The same thing happens in an internal combustion engine, which is why they always run at less than 100% efficiency.

 

[rude man]

The heat transfer would be greater than the change in potential energy, because some of the energy is lost due to friction and other effects (such as heat lost through conduction).

The heat transfer would be greater than the change in potential energy, which is the work done by the gas, because some of the heat went to raising the piston (p.e.) but some also went to raising the temperature of the gas: Q = ΔU + W where W = Δp.e. and ΔU ~ C_VΔT.