Question

If a gas expands at constant temperature, it indicates that:
a.) Kinetic energy of molecules decreases
b.) Pressure of the gas increases
c.) Kinetic energy of molecules remains same
d.) Number of molecules of gas increases

Answer 1

Hint: When we are going to deal with the expansion of gases, it is significant to be aware that both temperature and pressure govern the change in volume of the substance. Ideal Gas Equation allows us to calculate the pressure, volume, temperature, or moles of a gas.


Complete step by step solution: In the question it is given that a gas expands at constant temperature.
At constant temperature, pressure of the gas is inversely proportional to volume.
\[P\propto \frac{1}{V}\] (Boyle’s law).
Coming to given options, option A, Kinetic energy of molecules decreases. It is wrong, because at constant temperature, kinetic energy of the molecules does not change.
Coming to option B, pressure of the gas increases, it is also wrong because if there is no change in temperature of the gas, pressure of the gas is going to decrease.
Coming to option D, the number of molecules of gas increases, it is also wrong because when the temperature is constant the pressure decreases. If pressure decreases there is no change in number of moles of a gas.
Coming to option C, Kinetic energy of molecules remains the same. It is correct because at constant temperature kinetic energy of the gas remains the same.
\[\begin{align}
  & KE=\frac{3}{2}RT \\
 & KE\propto T \\
\end{align}\]
Therefore, if gas expands at a constant temperature the kinetic energy of the molecules remains the same.

So, the correction option is C.

Note: Don’t be confused with the relation between temperature and kinetic energy of the gas.
Kinetic energy of the gas is directly proportional to temperature of the gas. If the temperature of the gas increases the kinetic energy of the gas also increases.
\[KE\propto T\]