How much heat energy is transferred to or from the gas

[Meteo]

0.250 mol of a monatomic gas follows the process shown in the figure.

How much heat energy is transferred to or from the gas during process 1 to 2?

How much heat energy is transferred to or from the gas during process 2 to 3?

What is the total change in thermal energy of the gas?

I am not sure how to relate pressure and volume to heat energy.

I have $$pV=nRT$$ and $$\Delta E_{th}=W+Q$$

Also for the third question. would I just subtract the energy at point 3 from the energy at
point 1?

 

[Andrew Mason]

0.250 mol of a monatomic gas follows the process shown in the figure.

How much heat energy is transferred to or from the gas during process 1 to 2?
How much heat energy is transferred to or from the gas during process 2 to 3?
What is the total change in thermal energy of the gas?
I am not sure how to relate pressure and volume to heat energy.
I have $$pV=nRT$$ and $$\DeltaE_th=W+Q$$
Also for the third question. would I just subtract the energy at point 3 from the energy at point 1?

The change in internal (thermal) energy of the gas is:

$$\Delta U = nC_v\Delta T = \Delta Q + W$$ where W is the work done to the gas (use -W if W is the work done by the gas).

What is $C_v$ for an ideal monatomic gas?

AM

 

[quicknote]

I can provide a response to your questions by utilizing the first law of thermodynamics, which states that the change in thermal energy of a system is equal to the work done on the system plus the heat transferred to the system.

For the first question, the heat energy transferred during process 1 to 2 can be calculated by finding the difference in thermal energy between points 1 and 2. This can be done by using the equation \Delta E_{th}=W+Q and substituting the values of work and change in thermal energy from the given figure.

Similarly, for the second question, the heat energy transferred during process 2 to 3 can be calculated by finding the difference in thermal energy between points 2 and 3.

To answer the third question, you can calculate the total change in thermal energy of the gas by finding the difference between the thermal energy at point 3 and point 1. This will give you the total amount of heat energy transferred to or from the gas during the entire process.

In order to relate pressure and volume to heat energy, you can use the ideal gas law, pV=nRT, where p is pressure, V is volume, n is the number of moles of gas, R is the gas constant, and T is the temperature in Kelvin. This equation can be used to calculate the work done on the gas during a process, which can then be used in the first law of thermodynamics to calculate the change in thermal energy.

I hope this explanation helps in understanding how to calculate the heat energy transferred to or from a gas during a thermodynamic process.