A piston is cleverly designed so that it extracts the maximum amount of work out of a chemical reaction, by matching Pexternalto the Pinternalat all times. This 8cm diameter piston initially holds back 1 mol of gas occupying 1 L, and comes to rest after being pushed out a further 2 L at 25oC.After exactly half of the work has been done, the piston has travelled out a total ofa)10.0 cmb)11.2 cmc)14.5 cmd)20.0 cmCorrect answer is option 'C'. Can you explain this answer?

Question

Answer

Piston change in volume

V = of cylinder = πr²h

Answer

Answer

To solve this problem, we need to understand the concept of work done in a chemical reaction and how it relates to the movement of a piston.

1. Understanding the Concept:
- In a chemical reaction, work is done when a system undergoes a change in volume against an external pressure.
- The work done (W) can be calculated using the equation: W = -PΔV, where P is the external pressure and ΔV is the change in volume.
- For maximum work to be extracted, the external pressure (Pexternal) should match the internal pressure (Pinternal) at all times.

2. Given Information:
- Piston diameter = 8 cm, which means radius (r) = 4 cm = 0.04 m.
- Initial volume (V1) = 1 L = 0.001 m^3.
- Final volume (V2) = 1 L + 2 L = 3 L = 0.003 m^3.
- Temperature (T) = 25°C = 298 K.

3. Calculating the Internal Pressure:
- The internal pressure can be calculated using the ideal gas law: PV = nRT.
- Rearranging the equation, we get Pinternal = (nRT) / Vinternal, where n is the number of moles, R is the ideal gas constant, and Vinternal is the internal volume.
- Substituting the given values, we get Pinternal = (1 mol * 0.0821 L atm mol^(-1) K^(-1) * 298 K) / 0.001 m^3 = 24.4 atm.

4. Calculating the External Pressure:
- Since the external pressure should match the internal pressure at all times, Pexternal = Pinternal = 24.4 atm.

5. Calculating the Work Done:
- We know that half of the work has been done when the piston stops moving.
- Let's assume that the piston has moved out x cm at this point.
- The change in volume (ΔV) can be calculated as ΔV = V2 - V1 = (3 L - 1 L) = 2 L = 0.002 m^3.
- The work done can be calculated as W = -Pexternal * ΔV = -(24.4 atm * 0.002 m^3) = -0.0488 m^3 atm.

6. Calculating the Distance Travelled:
- The work done (W) can be calculated using the equation: W = F * d, where F is the force applied and d is the distance travelled.
- Since the force applied is constant, we can rewrite the equation as W = P * A * d, where P is the pressure and A is the cross-sectional area of the piston.
- Rearranging the equation, we get d = W / (P * A).
- Substituting the given values, we get d = (-0.0488 m^3 atm) / (24.4 atm * π * (0.04 m)^2) ≈ -0.199 m.

7. Converting the Distance to centimeters:
- Since the distance travelled can't be negative, we take the absolute value: d = 0.199 m.
- Converting meters to centimeters, we get d ≈ 19.9 cm.

8

Answer

Piston change in volume

V = of cylinder = πr²h

Similar JEE Doubts

At what speed a ball must be projected vertically upward so that distance travelled by it in 5thsecond is equal to distance travelled in sixth second (in m/s):- Correct answer is '49'. Can you explain this answer?

At what speed a ball must be projected vertically upward so that distance travelled by it in 5thsecond is equal to distance travelled in sixth second (in m/s):- Correct answer is '49'. Can you explain this answer?

Top Courses for JEEView all

Mock Tests for JEE Main and Advanced 2025

VITEEE: Subject Wise and Full Length MOCK Tests

BITSAT Mock Tests Series & Past Year Papers 2025

UGEE Mock Test Series 2025

Physics for JEE Main & Advanced

Top Courses for JEE

Top Courses for JEE

Related Content

JEE Courses

Mock Test Series

Past Year Papers

Additional Courses

Company