# How Is Internal Energy Calculated for an Ideal Gas Using Temperature Change?

• tuki
In summary, the conversation discusses the definition of change in internal energy, which is represented by the equation ΔU = Q - W. The work (W) can be calculated using the equation W = pΔV, but this only works if pressure is constant. In this case, the pressure is not constant, so the first law cannot be used to solve the problem. The conversation also mentions the concepts of heat energy (Q) and work done by the gas (W). It is noted that the change in internal energy of an ideal gas can be determined based on its change in temperature. Additionally, the molar heat capacity at constant volume of an ideal gas with 2 atoms is discussed. Finally, the ideal gas law is mentioned
tuki
Homework Statement
1.5 moles of two atom ideal gas is being heated so that pressure and volume change during the process. At the beginning pressure is at 336 kPa and volume is 12 Liters. In the end pressure is 439 kPa and volume is 14 Liters. What is change in internal energy?
Relevant Equations
Definition of change in internal energy
$$\Delta U = Q - W$$
Work done by pressure
$$W = \int_{V_1}^{V_2} p dV$$
I have the definition of change in internal energy.
$$\Delta U = Q - W$$
I can get the work by
$$W = \int_{V_1}^{V_2} p dV = p \Delta V$$
however the pressure isn't constant so this won't do.
## W ## is work done by the gas and ## Q ## is amount of heat energy brought into the system.
I'm not quite sure how do i get these? I think I'm stuck.

You don't (and can't) use the first law to do this because all you are given is the end points, but not the pressure and volume changes in between. So you must solve this problem only having the end point information.

What is the change in internal energy of an ideal gas in terms of its change in temperature?
What is the molar heat capacity at constant volume of an ideal gas having 2 atoms?
From the ideal gas law, what is PV equal to?

## 1. What is internal energy in an ideal gas?

The internal energy in an ideal gas is the total energy of all the particles within the gas, including their kinetic energy and potential energy. It is a measure of the gas's microscopic energy and is related to its temperature, pressure, and volume.

## 2. How is internal energy related to temperature in an ideal gas?

According to the ideal gas law, the temperature of an ideal gas is directly proportional to its internal energy. This means that as the temperature of the gas increases, so does its internal energy. Similarly, as the temperature decreases, the internal energy also decreases.

## 3. Can internal energy be changed in an ideal gas without changing its temperature?

Yes, internal energy can be changed in an ideal gas without changing its temperature. This can be achieved by changing the volume or pressure of the gas. For example, when a gas expands, its volume increases and its internal energy also increases. However, the temperature remains constant.

## 4. How is internal energy affected by the number of particles in an ideal gas?

The internal energy of an ideal gas is directly proportional to the number of particles present in the gas. This means that as the number of particles increases, so does the internal energy. Similarly, if the number of particles decreases, the internal energy also decreases.

## 5. What happens to the internal energy of an ideal gas during an adiabatic process?

In an adiabatic process, there is no heat exchange between the gas and its surroundings. This means that the internal energy of the gas remains constant. However, the temperature and pressure of the gas can change due to the work done on or by the gas, as described by the first law of thermodynamics.

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