Ideal Gas Equation | Find Gas Temperature

• keemosabi
In summary, the problem involves compressing three moles of an ideal gas from 5.5 * 10^-2 to 2.8 * 10^-2 m^3 while keeping the temperature constant. 6.5 * 10^3 J of work is done on the gas and heat is removed. The task is to find the temperature of the gas using the equation pv=nRT, where work is equal to force times distance. This is known as an isothermal expansion and can be solved by looking at the relationship between pressure, volume, and energy.
keemosabi

Homework Statement

Three moles of an ideal gas are compressed from 5.5 * 10^-2 to 2.8 * 10^-2 m3. During the compression, 6.5 * 10^3 J of work is done on the gas, and heat is removed to keep the temperature of the gas constant at all times.

Find the temperature of the gas.

pv=nRT

The Attempt at a Solution

I plugged into the above equation so I have p(.028)=3(8.31)T but I don't know how to solve this since there are two variables.

You also need a relationship between pressure, volume an energy
hint - work = force * distance

mgb_phys said:
You also need a relationship between pressure, volume an energy
hint - work = force * distance

U = f*d+Q
U = A*p*d+Q
U = p*V+QDoes that seem right?

Last edited by a moderator:

1. What is the ideal gas equation?

The ideal gas equation, also known as the ideal gas law, is a mathematical relationship between the pressure, volume, temperature, and number of moles of a gas. It is represented by the formula PV = nRT, where P is pressure in atmospheres, V is volume in liters, n is the number of moles, R is the ideal gas constant, and T is temperature in Kelvin.

2. How do you find the temperature using the ideal gas equation?

To find the temperature using the ideal gas equation, you can rearrange the formula as T = PV/nR. This means you divide the product of pressure and volume by the number of moles and the ideal gas constant. Be sure to use the appropriate units for each variable (atm for pressure, L for volume, mol for moles, and J/mol·K for the ideal gas constant).

3. When can the ideal gas equation be used?

The ideal gas equation can be used to calculate the properties of an ideal gas at any state (temperature, pressure, and volume) as long as the gas behaves ideally. This means that the gas particles are not interacting with each other and there are no significant intermolecular forces.

4. Can the ideal gas equation be used for all gases?

No, the ideal gas equation is only applicable to ideal gases. In reality, all gases deviate from ideal behavior to some extent, especially at high pressures and low temperatures. However, many real gases can be approximated as ideal gases under certain conditions.

5. How does changing the pressure or volume of a gas affect its temperature according to the ideal gas equation?

According to the ideal gas equation, if the pressure of a gas is increased while keeping the volume constant, the temperature will also increase. Similarly, if the volume is increased while keeping the pressure constant, the temperature will decrease. This is known as Boyle's Law, which is a special case of the ideal gas equation.

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