What is the power of a car engine?

• greypilgrim
In summary: What you are saying contradicts the first sentence of the book.Yes, the piston is connected through the transmission system to the road wheels, so the resistance is a lot more than that.In summary, the engine performs work and produces power by moving the piston at 3000 rpm.
greypilgrim

Homework Statement

The volume displacement in a car engine is 2000 cm3. During the power stroke, the mean pressure inside the cylinder is 15 bar.
1. Compute the work performed by the engine in one revolution.
2. Compute the engine's power assuming it runs at 3000 rpm.

Homework Equations

$$W=-p\cdot \Delta V=-3000\text{ J}$$
$$P=\frac{3000\cdot\left|W\right|}{60 \text{ s}}=150\text{ kW}$$

The Attempt at a Solution

Above numbers are the solutions given by the book. However I'm not sure if they are correct.
1. Shouldn't the pressure exerted from the outside by the piston be relevant here, since this is what the gas is working against? Or do we need to assume an equilibrium between inside and outside pressure in a thermodynamic treatment? Is this justified in reality?
2. Usual car engines are four-stroke, so there's a power stroke only in every second revolution. Shouldn't both numbers need to be divided by 2 because of this?

You make a good point about the way a four cycle engine works. Perhaps something the author did not consider.

greypilgrim said:
Shouldn't the pressure exerted from the outside by the piston be relevant here, since this is what the gas is working against?
Not sure which point you are making.
If you are concerned about atmospheric pressure, the 15bar might well refer to gauge pressure, not absolute.
If you feel there would be a difference between the pressure in the cylinder and the backpressure from the piston, no - action and reaction are equal and opposite.
If you mean the force transmitted through the piston would be less than pressure x area in the cylinder,yes, but only in respect of the net force required to accelerate the piston, which would be quite small.

haruspex said:
If you feel there would be a difference between the pressure in the cylinder and the backpressure from the piston, no - action and reaction are equal and opposite.
Let's look at an isolated cylinder with atmospheric pressure in- and outside (1 bar), so the piston is at rest. Now combustion is ignited, almost instantly increasing the inside pressure to 15 bar. If the piston now moves, which one is the relevant pressure to compute the work, the 15 bar inside or the 1 bar outside?

greypilgrim said:
Let's look at an isolated cylinder with atmospheric pressure in- and outside (1 bar), so the piston is at rest. Now combustion is ignited, almost instantly increasing the inside pressure to 15 bar. If the piston now moves, which one is the relevant pressure to compute the work, the 15 bar inside or the 1 bar outside?
The 15 bar inside. It is doing work against a resistance, which has little to do with the 1 bar ambient. If you were to disconnect the load, it would not reach 15 bar.

haruspex said:
It is doing work against a resistance, which has little to do with the 1 bar ambient.
Why? Isn't this resistance exactly given by the 1 bar times area?

What about following more symmetric situation: Suppose we have a closed cylinder with a (thermally isolating) piston in its centre that is fixed at first. We fill half ##A## with gas up to a pressure of ##p_A=1\text{ bar}##, half ##B## up to ##p_A=15\text{ bar}##. Then the piston is released.
For simplicity, let's look at a very small displacement ##\Delta V>0## after the release such that the pressures haven't changed considerably. According to you, half ##B## loses the energy
$$W_B=-p_B\cdot \Delta V\enspace.$$
However, the energy of the other half increases by
$$W_A=-p_A\cdot (-\Delta V)=p_A\cdot \Delta V\enspace$$
Since ##p_B\gg p_A## this obviously violates conservation of energy.

greypilgrim said:
Isn't this resistance exactly given by the 1 bar times area?
No, the piston is connected through the transmission system to the road wheels, so the resistance is a lot more than that.
If you disconnect the load completely, so there is just a piston with nothing restraining it, it will accelerate hugely and go flying through the air. You can apply ΔpA=F=ma to the piston to find its acceleration, but the backpressure is still 15bar.

scottdave

1. What is the power of a car engine?

The power of a car engine refers to the amount of energy it can produce in a given amount of time. It is typically measured in units of horsepower (hp) or kilowatts (kW).

2. How is the power of a car engine determined?

The power of a car engine is determined by several factors, including the size and number of cylinders, the type of fuel and ignition system, and the efficiency of the overall design. The engine's power can be increased through modifications such as turbocharging or adding performance parts.

3. What is the difference between horsepower and kilowatts?

Horsepower and kilowatts are both units of power, but they are used to measure different types of energy. Horsepower is the traditional unit of measurement for engine power, while kilowatts are used to measure the power output of electric motors.

4. How does the power of a car engine affect its performance?

The power of a car engine directly affects its performance, as it determines the amount of torque (or rotational force) that can be produced. A more powerful engine can accelerate faster and maintain higher speeds, but it may also consume more fuel.

5. Is higher engine power always better?

Not necessarily. While a more powerful engine can provide better performance, it also comes with a higher cost and potential drawbacks such as decreased fuel efficiency and increased emissions. It is important to consider your specific needs and driving habits when choosing a car with a certain level of engine power.

• Introductory Physics Homework Help
Replies
1
Views
553
• Introductory Physics Homework Help
Replies
20
Views
2K
• Introductory Physics Homework Help
Replies
8
Views
2K
• Introductory Physics Homework Help
Replies
5
Views
3K
• Introductory Physics Homework Help
Replies
5
Views
1K
• Introductory Physics Homework Help
Replies
8
Views
836
• Introductory Physics Homework Help
Replies
2
Views
986
• Introductory Physics Homework Help
Replies
5
Views
377
• Introductory Physics Homework Help
Replies
1
Views
2K
• Introductory Physics Homework Help
Replies
15
Views
1K