# A gas fills half of a conatainer and the gas is heated at the bottom so that the tempature doubles, but the piston is held in place. What happens to the gas?

Nov 6, 2016

The pressure doubles.

#### Explanation:

Hi. As you say, the gas fills half of the container.

1. The gas will occupy the whole of the volume of the container (as it is closed).

2. Now, as the gas is heated, the temperature rises. Thus the gas molecules attain kinetic energy,

3. Due to which they start moving randomly very fast.

4. Thus as the container is closed, the probability of gas molecules hitting the sides of the container increases and the pressure increases.

5. Even though moles remain constant, i.e. the amount of gas in the container remains constant (as the piston is held in place).

You can visualize this with

$P V = n R T$

$P = \text{pressure}$
$n = \text{moles}$
$V = \text{volume of container}$
R = "constant" = "0.0821 L" *"atm"//("mol"·"K")
$T = \text{temperature}$

Now, if $V$ is constant, $R$ is constant, and $n$ (moles) is constant,

We can consider these AS SOME CONSTANT $K$

$P = \left(\frac{n R}{V}\right) T = K T$

Now let the temperature ${T}_{1} = 2 T$ as per the given condition.

The pressure becomes ${P}_{1}$ and dividing them

$\frac{P}{P} _ 1 = \frac{K T}{2 K T}$

$\frac{P}{P} _ 1 = \frac{1}{2}$

${P}_{1} = 2 P$

Thus the pressure doubles.