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Question: An ideal gas expands from \(1 \times {10^{ - 3}}\) to \(1 \times {10^{ - 2}}{m^2}\) at \(300K\) agai...

An ideal gas expands from 1×10−31 \times {10^{ - 3}} to 1×10−2m21 \times {10^{ - 2}}{m^2} at 300K300K against a constant pressure of 1×105Nm−21 \times {10^5}N{m^{ - 2}}. The work done is?
A. 270kJ270kJ
B. −900kJ - 900kJ
C. −900J - 900J
D. 900kJ900kJ

Explanation

Solution

When the gas is expanded at constant pressure, heat should be transferred into the system at a certain rate and the process is known as Isobaric Expansion. Isobaric expansion requires heat transfer during the expansion to keep the pressure constant. The formula of the work done due to constant pressure is to be used here.
Formula used:
W=−PΔVW = - P\Delta V
Where WW is the work done, PP is pressure, ΔV\Delta V is the change in volume during the process.

Complete step by step answer:
The work done by a system or upon a system can be written in terms of pressure. It is the product of pressure and change in the volume of the container in which the gas is kept.
The work done due to constant pressure is,
W=−PΔVW = - P\Delta V........ (1)
Where WW is the work done, PP is pressure, ΔV\Delta V is the change in volume during the process.
We get W=−P(V2−V1)W = - P(V2 - V1) ……….. (2)
Given that,
V1=1×10−3m2V1 = 1 \times {10^{ - 3}}{m^2}
V2=1×10−2m2V2 = 1 \times {10^{ - 2}}{m^2}
P=1×105Nm−2P = 1 \times {10^5}N{m^{ - 2}}
Put these values in equation (2)
W=−1×105(1×10−2−1×10−3)W = - 1 \times {10^5}(1 \times {10^{ - 2}} - 1 \times {10^{ - 3}})
W=−1×105(10×10−3−1×10−3)W = - 1 \times {10^5}(10 \times {10^{ - 3}} - 1 \times {10^{ - 3}})
W=−1×105(9×10−3)W = - 1 \times {10^5}(9 \times {10^{ - 3}})
W=−900JW = - 900J

So, the correct answer is “Option C”.

Note:
In an ideal gas, no intermolecular force of attraction exists since the molecules of ideal gas travel so fast and are far away from each other so they do not interact with each other. Ideal gas does not exist in nature but gases do behave ideally at high temperature and low pressure.
There are different types of expansion in gases such as isothermal expansion, free expansion of gases, and adiabatic expansion. Isothermal expansion happens at constant temperature and free expansion of gases occurs when gas is subjected to expansion in a vacuum. In adiabatic expansion, there is no change in heat and according to the first law of thermodynamics in adiabatic expansion, internal energy would be equal to work done.
When the gas expands internal energy depends upon temperature that is why ideal gas expands freely because its temperature does not change.