Calculating Internal Energy & Temperature Change of Ideal Gas

In summary, the change in internal energy of an ideal gas is calculated by using the formula U=3/2 nRT. To find the change in temperature, the equations Q=8.314(1)(T) and Q=8.314(2)(T) are set up and solved. The final temperature is found by subtracting the two answers. The net amount of heat transferred to the gas is 2.95x10^6J. The first law states that the change in internal energy is equal to the net amount of heat transferred minus the work done, which in this case is 7.95x10^6J.
  • #1
Nick88

Homework Statement


What is the change in internal energy (in Joules) of an ideal gas that does 4.675x10^5J of work, while 2.95x10^6J of heat is transferred into the system and 7.95x10^6J of heat is transferred from the system to the environment? Calculate the change in temperature of the two moles of the gas. (R=8.314 J/mol.k)

Homework Equations


Formulas on equation sheet relating to concept: U=3/2 nRT, change in U=Q-W

The Attempt at a Solution


Me and my friend attempted two different ways, I'm probably wrong but my setup was
4.675x10^5=8.314(1)(T)
2.95x10^6=8.314(1)(T)
I found the two answers and added then together and did 7.95x10^6=8.314(2)(T) found this answer, then subtracted the two answers to get a final temperature.
 
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  • #2
What is the net amount of heat transferred to the gas? From the first law, what is the change in internal energy?
 

1. How do you calculate the internal energy of an ideal gas?

The internal energy of an ideal gas can be calculated using the equation U = 3/2 * nRT, where U is the internal energy, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin.

2. What is the relationship between internal energy and temperature change in an ideal gas?

According to the Ideal Gas Law, the internal energy of an ideal gas is directly proportional to its temperature. This means that as the temperature of an ideal gas increases, so does its internal energy.

3. How do you calculate the change in internal energy of an ideal gas?

The change in internal energy of an ideal gas can be calculated using the equation ΔU = nCΔT, where ΔU is the change in internal energy, n is the number of moles, C is the molar specific heat capacity, and ΔT is the change in temperature.

4. What is the difference between internal energy and enthalpy of an ideal gas?

Internal energy refers to the total energy of a system due to the movement and interactions of its particles, while enthalpy takes into account the pressure and volume of the system. In an ideal gas, the enthalpy is equal to the internal energy plus the product of pressure and volume.

5. How does the change in temperature of an ideal gas affect its internal energy?

The change in temperature of an ideal gas has a direct effect on its internal energy. As the temperature increases, the internal energy also increases. Conversely, a decrease in temperature results in a decrease in internal energy.

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