# How can I calculate the efficiency of an air-powered car?

An air-powered car is powered using high pressure compressed air stored in a tank. The pressurized tank is connected to an air-powered engine. The volume of the tank is 0.3 m3, and the initial temperature and pressure of air inside the tank is 20°C and 30 MPa, respectively. What is the efficiency of the car?

I feel like this problem is missing some relevant information. Efficiency is the ratio of work done to heat provided. None of that information is given; there is no information on the engine itself, its process, or any work done.

Am I misunderstanding this question?

## 1 Answer

Like you, I have problems with this question. The first is that $efficiency$ is usually defined for a cyclic process in which the working substance is returned to its initial state. You don't have information about how the cycle is completed, so you can't calculate this efficiency (which would be less than 100%).

Thinking about just the expansion of the gas, if this were isothermal (same temperature) and could be accomplished by a single stroke of a piston (couldn't be in practice), then all the work done (51 MJ, I think, assuming isothermal expansion from a pressure of 50 MPa to 0.10 MPa) would be provided by heat flowing into the trapped air from the surroundings (which I'm supposing to be at a temperature just higher than 20°C). But, as I said above, I don't think this provides an adequate basis for calculating efficiency.

• It's what I thought. I have an assignment full of such questions and its been driving me nuts - think I'll have to get more clarification from classmates or the teacher. Thanks! – Emmanuel Coleman Nov 4 '17 at 20:41
• Please let us know how you are advised to do the calculation! – Philip Wood Nov 5 '17 at 8:50