# Gas expansion at constant pressure

• wavingerwin
In summary, the problem involves expanding 2 moles of monoatomic gas at 300 K and 0.02 m3 to twice the volume at constant pressure, then adiabatically until reaching 300 K again. The final volume is 0.061 m3 and the heat supplied to the system is 5 kJ. The change in internal energy is also 5 kJ. The expansion at constant pressure is achieved by applying heat and raising the temperature of the gas. The specific heat capacity at constant pressure is needed to calculate the heat supplied, but it is not given in the problem. It can be found by looking after the specific heat capacity at constant pressure (cp) for a monoatomic ideal gas.
wavingerwin

## Homework Statement

2 moles of gas at 300 K at 0.02 m3 is expanded to twice the original volume at constant pressure, and then adiabatically until T = 300 K again.

assume monatomic gas. assume ideal.

determine the final volume

determine the heat supplied to the overall process

determine change in internal energy

## Homework Equations

$$PV = nRT$$
$$TV^{\gamma-1} = TV^{\gamma-1}$$

## The Attempt at a Solution

State 1
n = 2
V = 0.02
R = 8.31
T = 300

P = 249.3 kPa

State 2
P = 249.3
V = 0.04

T = 600 K

State 3
T = 300
monatomic therefore $$\gamma=5/3$$

V = 0.061

so final volume is 0.061 m3

I am struggling to find the "heat supplied" to the system. Since from state 2 to 3 the process is adiabatic, Q = 0.

So the only heat transfer occur from state 1 to 2.

Would it just be equal to the work?
so Q = W = P(V2-V1) = 249300 x 0.02 = 5 kJ?

and so the change in internal energy must also be be 5 kJ?

thank you in advance.

How can you make the gas expand at constant pressure?

ehild

Hi ehild

by applying heat and raising its temperature.

However, I don't have/know an equation that equates total heating applied (Q) to the raise in temperature..

What about specific heat capacity at constant pressure?

ehild

specific heat, c would equal du/dT

so I guess the heat supplied, q, would equal change in u = c dT

but c is not given in the question.

It is 2 moles of mono-atomic ideal gas. Look after cp.

ehild

## 1. What is gas expansion at constant pressure?

Gas expansion at constant pressure refers to the process of a gas increasing in volume while the pressure remains constant. This can occur when the gas is heated or when the external pressure on the gas is reduced.

## 2. How does gas expansion at constant pressure occur?

Gas expansion at constant pressure occurs through the transfer of energy in the form of heat. When the temperature of a gas increases, the molecules move faster and collide with each other and the walls of their container, causing the gas to expand.

## 3. What is the relationship between volume and temperature in gas expansion at constant pressure?

In gas expansion at constant pressure, the volume of the gas is directly proportional to the temperature. This means that as the temperature increases, the volume of the gas also increases.

## 4. What is the effect of constant pressure on gas expansion?

Constant pressure allows for gas expansion to occur without any change in pressure. This means that as the gas expands, it does not exert any additional force on its container, allowing for a controlled expansion.

## 5. What are some real-life examples of gas expansion at constant pressure?

A common example of gas expansion at constant pressure is the use of a hot air balloon. The air inside the balloon is heated, causing it to expand and become less dense than the surrounding air, allowing the balloon to rise. Another example is the use of steam engines, where steam is heated at constant pressure to produce mechanical work.

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