Question

A gas expands from 1 liter to 3 liter at atmospheric pressure. The work done by the gas is about (A) \(200 \mathrm{~J}\) (B) \(2 \mathrm{~J}\) (C) \(300 \mathrm{~J}\) (D) \(2 \times 10^{5} \mathrm{~J}\)

Short answer

The work done by the gas when it expands from 1 liter to 3 liters at atmospheric pressure can be calculated using the formula: \(W = P \times \Delta V\). After converting the pressure to pascals and the volume change to cubic meters, we get \(W = (101325 ~Pa) \times (0.002 ~m^3) = 202.65 ~J\). Therefore, the correct option is (A) \(200 \mathrm{~J}\).

Step-by-step solution

Convert atmospheric pressure to pascals

At standard atmospheric pressure, 1 atmosphere is equal to 101325 pascals (Pa). Therefore, we will first convert the pressure to pascals: \(1~ atm = 101325 ~Pa\)

Calculate volume change

The gas expands from 1 liter to 3 liters, so the volume change can be calculated as follows: \[\Delta V = V_{final} - V_{initial} = 3L - 1L = 2L\]

Convert liters to cubic meters

Gases usually have their volume measured in liters. However, to calculate work in the SI unit (Joule), we need to have volumes in cubic meters (m³). There are 1,000 liters in a cubic meter, so our volume change will be: \(\Delta V = 2L \times \frac{1 m^{3}}{1000 L} = 0.002 m^{3}\)

Calculate work

Now that we have the pressure in pascals and the volume change in cubic meters, we can calculate the work done by the gas using the formula: \[W = P \times \Delta V\] \[W = (101325 ~Pa) \times (0.002 ~m^3)\] \[W = 202.65 ~J\] Since the work done by the gas is about 202.65 J, the correct option is: (A) \(200 \mathrm{~J}\)