# At constant volume in a closed container, how do you explain that increasing temperature leads to increasing gas pressure?

##### 1 Answer

There are two ways to explain it.

Here's the context.

At a constant volume, we have a rigid container. We can keep the quantity of gas constant simply by making sure the container is sealed tight.

*Overall, we have a rigid, closed container.*

**CONCEPTUAL WAY**

Heating the gas inside will make the gas particles move faster, and they will collide with the walls more often.

**Pressure** is defined as the *force per unit area*:

#P = F/A#

So, the ** higher** the temperature, the

**the speed in general for each gas particle, and the**

*higher***the force at which it hits the walls of the container.**

*stronger*Therefore, the pressure is ** higher**.

**MATHEMATICAL WAY**

From the ideal gas law:

#PV = nRT#

Keeping volume and mols of gas constant, we have the initial and final states as:

#P_1V = nRT_1#

#P_2V = nRT_2#

Dividing these equations, we get:

#P_2/P_1cancel((V/V)) = cancel(((nR)/(nR))) T_2/T_1#

#=> P_2/T_2 = P_1/T_1 = "const"#

If the temperature is increased,

If

Therefore, ** increased**.