Understanding the Problem

The task is to calculate the work done by a piston when it moves a certain distance under a given pressure. The initial problem presents this situation with specific values but doesn't use the appropriate units, making the calculation a bit more complex than necessary. Here, we’ll provide a clear and detailed solution using the correct units and units conversion factors.

Given Data:

Area of the piston, A 60 cm2 0.006 m2Distance moved by the piston, d 20 cm 0.2 mPressure, P 3 atm 3 × 101325 Pa (1 atm 101325 Pa)

Step 1: Calculating the Force

First, we need to find the force exerted by the pressure on the piston. The formula for force is F Pressure × Area.

F 3 × 101325 Pa × 0.006 m2 1823.95 N

Step 2: Calculating the Work Done

Work is calculated using the formula Work Force × Distance.

W 1823.95 N × 0.2 m 364.79 J

Step 3: Converting Joules to Calories

The conversion factor from joules to calories is 1 calorie 4.184 joules. Therefore,

364.79 J / 4.184 cal/J ≈ 87.18 calories

Conclusion

The final result is that the work done is approximately 364.79 joules or 87.18 calories. This process demonstrates the importance of converting all measurements to standard units prior to performing any calculations in physics and engineering problems.

Related Calculations

The provided data assumes that the pressure at the other end of the piston is zero, and that the displacement is entirely in the direction of the force. Here is a step-by-step guide to the calculations:

Force (F) Pressure (P) × Area (A) 3 atm × 0.006 m2

Since 1 atm 101325 Pa, F 3 × 101325 Pa × 0.006 m2 1823.95 N

Work (W) Force (F) × Distance (d) 1823.95 N × 0.2 m 364.79 J

Converting to calories, 364.79 J / 4.184 cal/J ≈ 87.18 calories

Summary

This article has illustrated the correct method of calculating the work done by a piston in both joules and calories, demonstrating the importance of using appropriate units and conversion factors in scientific calculations. Understanding these principles can help in a wide range of engineering and physics applications.