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# In isothermal ideal gas compression :A. $w{\text{ }}is + ve$B. $\Delta {\rm H}$ is zeroC. $\Delta {S_{gas}}is + ve$ D. $\Delta Gis + ve$

Last updated date: 18th Jun 2024
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Hint: An isothermal process is one in which the pressure and volume of the system change but temperature remains constant . When compression of an ideal gas takes place at constant temperature it is known as isothermal compression .

Suppose we have an ideal gas enclosed in a cylinder provided with a piston and having conducting walls . When we compress the gas slowly , the heat which is produced due to the work done on the gas is transferred to the surroundings so that the temperature of the gas remains constant , that is , the process takes place isothermally .
The temperature change and hence the change in internal energy (since it is a function of temperature ) in this process is zero .
The work done in isothermal process is given by
$w = - 2.303nRT\log \dfrac{{{V_2}}}{{{V_1}}}$
The negative sign shows work of expansion .
But since to compress a gas work is done on the system , so that pressure is increased and volume is decreased the work done is positive .

So, the correct answer is Option A .

Note:
here are certain conditions for isothermal compression to take place which should be kept in mind :
The walls of the container should be perfectly conducting so that free exchange of heat between the system and surroundings takes place .
When we compress a gas it should be done very slowly , so as to provide sufficient time for the exchange of heat .