Question

A gas in an airtight container is heated from ${{25}^{0}}C$ to${{90}^{0}}C$.The density of the gas will

A. Increase slightly
B. Increase considerably
C. Remain the same
D. Decrease slightly

Answer 1

Density of an object can be given by:
$Density(\rho )=\dfrac{Mass(m)}{Volume(V)}$
As per Charles law, Volume is directly proportional to Temperature.
$V\propto T$
An airtight container is such a container in which no air from the external environment or surrounding can enter into the container. Therefore, the gases present in it will occupy a constant volume, the volume of the container.

Complete answer:
Since the amount of gas taken is fixed, the Mass$\left( m \right)$of the gas inside the air tight container will be constant.
$\Rightarrow Mass=constant$
Also, the container used is airtight due to which the volume of the gas inside the container will also remain constant despite the change in volume expected due to change in temperature as volume is directly proportional to temperature.
$\Rightarrow Volume=constant$
Since,
$Density(\rho )=\dfrac{Mass(m)}{Volume(V)}$
And both the terms in the RHS are constants, then the density will also remain constant for the equality to persist.

Hence the correct option would be option (C) Remain the same.

Note :
If the given container was not airtight then:
1. The density would have slightly increased with a slight decrease in temperature.
2. The density would have increased considerably if the temperature was decreased massively.
3. The density would have decreased slightly if the temperature was increased (similar to the change as given in the question i.e. ${{25}^{0}}C$ to ${{90}^{0}}C$).
Since volume is directly proportional to temperature.