---
title: "Gas under piston: pressure, volume doubled"
subject: "Fundamental of Thermodynamics & Heat Transfer"
chapter: 1
key: "semester_2/fundamental_of_thermodynamics_and_heat_transfer:gas-cylinder-piston-pressure-490n"
source: https://www.bctengineer.com/q/semester_2/fundamental_of_thermodynamics_and_heat_transfer/gas-cylinder-piston-pressure-490n
site: BCT Engineering
---

# Gas under piston: pressure, volume doubled

Fundamental of Thermodynamics & Heat Transfer · Chapter 1: Introduction

- Asked in: 2071 Magh
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_2/fundamental_of_thermodynamics_and_heat_transfer/gas-cylinder-piston-pressure-490n
- Whole chapter: https://www.bctengineer.com/md/semester_2/fundamental_of_thermodynamics_and_heat_transfer/chapter-1

## Question

A cylinder encloses a gas with a piston as shown in Figure P.2. The area of piston is 0.01 m². Take the atmospheric pressure to be 0.101 MPa and the local gravitational acceleration as 9.81 m/s². If the weight of the piston is 490.50 N, what is the gas pressure? Will the gas pressure change if the gas volume beneath the piston is double?
[Figure P.2: vertical cylinder of gas closed by a piston with a small weight/rod on top.]

## Short answer

P = P_atm + W/A = 101000 + 490.5/0.01 = 150.05 kPa. Pressure does not change when volume doubles; piston equilibrium is set solely by external loads.

## Answer

**Given:** A = 0.01 m², P_atm = 0.101 MPa = 101 kPa, piston weight W = 490.5 N. (Only the piston weight is taken to act on the gas; the small rod/weight on top is neglected.)

**Force balance on the piston** (in equilibrium):  
P·A = P_atm·A + W

P = P_atm + W/A  
P = 101 000 + 490.5/0.01 = 101 000 + 49 050 = 150 050 Pa

**Answer: Gas pressure = 150.05 kPa ≈ 0.15 MPa.**

#### Does the pressure change if the gas volume is doubled?
**No.** The piston is free and in equilibrium, so the pressure is fixed only by the force balance: P = P_atm + W/A. This does not contain volume. If the gas volume doubles (for example by heating), the piston just moves up and the pressure remains 150.05 kPa (constant-pressure process), as long as the piston does not hit stops or a spring.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. For a free piston in equilibrium, the gas pressure is given by
   A. P = P_atm - W/A
   B. P = W/A
   C. P = P_atm + W/A
   D. P = P_atm x W
   Answer: C. Gas force upward equals atmospheric force plus piston weight downward: PA = P_atm A + W. (Key point: Force balance)

2. With A = 0.01 m^2, P_atm = 101 kPa and W = 490.5 N, the gas pressure is
   A. 49.05 kPa
   B. 101 kPa
   C. 490.5 kPa
   D. 150.05 kPa
   Answer: D. P = 101 000 + 490.5/0.01 = 150 050 Pa. (Key point: Pressure value)

3. If the gas volume under the piston doubles, the pressure
   A. stays the same, as it is fixed by the force balance
   B. doubles
   C. halves
   D. becomes equal to P_atm
   Answer: A. P = P_atm + W/A has no volume term; the piston simply rises at constant pressure. (Key point: Effect of volume)

4. When would the pressure NOT stay constant as volume increases?
   A. If the gas is heated slowly
   B. If the piston is frictionless
   C. If the piston meets stops or a spring
   D. If the atmosphere is cold
   Answer: C. Stops or a spring add extra forces, so the force balance no longer fixes P. (Key point: Condition for constant pressure)

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