Question

How much work to be done in decreasing the volume of an ideal gas by an amount of $2.4 \times {10^{ - 4}}{m^3}$ at normal temperature and constant normal pressure of $1 \times {10^5}N/{m^2}$?
A. $28Joule$
B. $27Joule$
C. $25Joule$
D. $24Joule$

Answer 1

Hint: As the volume of an ideal gas decreases at Normal Temperature-Pressure conditions (NTP) in the given question, and the value of work done varies with the conditions of the system and surroundings. Hence, it is possible to calculate the required work done by using the formula of Pressure-Volume work and the volume change provided in the question.

Formula used:
The formula used for calculating work done in this problem is: -
$Workdone = W = P\Delta V$

Complete answer:
The volume of an ideal gas is decreased at normal atmospheric pressure of $P = 1 \times {10^5}N/{m^2}$ (given)

Since, the volume of an ideal gas is decreased, therefore, change in volume can be given as $\Delta V = \;\;2.4 \times {10^{ - 4}}{m^3}$ (given)

Now, we know that Pressure-Volume Work in thermodynamics is defined as: -
$Workdone = W = P\Delta V$

Substituting the value of $P$ and $\Delta V$ in the above expression, we get
$ \Rightarrow W = 1 \times {10^5}\left( {2.4 \times {{10}^{ - 4}}} \right)$
$ \Rightarrow W = 2.4 \times {10^5} \times {10^{ - 4}}$

On further calculation, we get
$ \Rightarrow W = 2.4 \times 10 = 24J$

Thus, $24Joule$ work is to be done in decreasing the volume of an ideal gas at normal temperature and pressure. Hence, the correct option is (D) $24Joule$.

Note: To calculate the amount of work done required in decreasing the volume of an ideal gas by a given amount in the given thermodynamic system, utilise the formula $W = P\Delta V$ . It is recommended to apply appropriate mathematical relations to solve this kind of conceptually based numerical problem in order to obtain an accurate answer.