(question pool) During the compression stroke in a four-stroke engine cycle, a cylinder is compressed from a volume of 445 mL to a volume of 75 mL with an external pressure of 13.0 atm. What is the work done on the gas inside the cylinder during this compression stroke? Report your answer to three significant figures.  *Given:*

In this problem, we are asked to calculate the **work done on the gas** during the compression stroke of a four-stroke engine cycle. The **work** done in a gas compression or expansion is related to the **change in volume** and **pressure**.

We are given:
- Initial volume \( V_1 = 445 \, \text{mL} \)
- Final volume \( V_2 = 75 \, \text{mL} \)
- External pressure \( P = 13.0 \, \text{atm} \)

### Formula for work done in compression:

The work done on a gas at constant pressure is calculated by:

\[
W = -P \Delta V
\]

where:
- \( W \) is the work done on the gas,
- \( P \) is the external pressure,
- \( \Delta V = V_2 - V_1 \) is the change in volume (final volume minus initial volume).

Here the work is negative because the gas is being compressed (work is done **on** the gas).

#### Step 1: Convert volumes to liters
We need to convert milliliters (mL) to liters (L), since 1 atm L = 101.3 J.

\[
V_1 = 445 \, \text{mL} = 0.445 \, \text{L}
\]
\[
V_2 = 75 \, \text{mL} = 0.075 \, \text{L}
\]

#### Step 2: Calculate the change in volume (\( \Delta V \))

\[
\Delta V = V_2 - V_1 = 0.075 \, \text{L} - 0.445 \, \text{L} = -0.370 \, \text{L}
\]

#### Step 3: Apply the formula for work

Now, using the formula \( W = -P \Delta V \):

\[
W = - (13.0 \, \text{atm}) \times (-0.370 \, \text{L})
\]

\[
W = 4.81 \, \text{L atm}
\]

#### Step 4: Convert the work to joules

To convert \( \text{L atm} \) to joules, we use the conversion factor \( 1 \, \text{L atm} = 101.3 \, \text{J} \):

\[
W = 4.81 \, \text{L atm} \times 101.3 \, \text{J/L atm}
\]

\[
W = 487.253 \, \text{J}
\]

#### Step 5: Report the final answer to three significant figures

\[
W = 487 \, \text{J}
\]

### Final Answer:
The work done on the gas is **487 J**.

Would you like a detailed breakdown of any part of this process? 

Here are five related questions you might explore:
1. How does the work change if the pressure is doubled?
2. What would the work be if the volumes were in reverse?
3. How does the type of gas affect the work done in such cycles?
4. Can you calculate work done in an adiabatic process?
5. How does this problem relate to the first law of thermodynamics?

**Tip:** Always check your units when working with gases to ensure consistency, especially when converting between mL, L, atm, and joules.

During the compression stroke in a four-stroke engine cycle, a cylinder is compressed from a volume of 445 mL to a volume of 75 mL with an external pressure of 13.0 atm. What is the work done on the gas inside the cylinder during this compression stroke? Report your answer to three significant figures.

Learn how to calculate the work done on gas during the compression stroke in a four-stroke engine cycle. This problem involves compressing gas from 445 mL to 75 mL under 13.0 atm pressure, with detailed steps including work-energy calculations and gas law applications. Suitable for advanced high school students studying thermodynamics and physics.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation