Change in heat and internal energy

In summary: Therefore, ΔQ=mCv(T3-T1) represents the change in internal energy of the system. The work done by the gas can be calculated by finding the area under the line from points 2 to 3 on a PV diagram. This can be done by using the ideal gas law, PV=nRT, to determine the values of V at each vertex and then deriving a formula for ΔW in terms of P, T, n, and R. Make sure to consider the sign convention being used when determining the sign of ΔQ and ΔW. In summary, the equation ΔQ=mCv(T3-T1) represents the change in internal energy of an ideal gas, and the work done by the gas can be calculated
  • #1
Homework Statement
What is the change in heat and internal energy in this PV diagram (attached link) from T2 to T3 (T represents temperature)?
Relevant Equations
ΔQ=mC(T3-T1)
Δu=ΔQ + Δw
ΔQ=mC(T3-T1)

But, will this C be Cp or Cv. Both pressure and volume changes. So, neither of them can be.

Feeling so confused
 

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  • #2
Calculate the work from 2-3 which will be the area under the line from 2-3( trapezium area) and you know the change in internal energy= Cv(T2-T3) and u will get ∆Q
 
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  • #3
Note this is a full cycle. You start at point 1 and finish at point 1. So the system's final state is the same as its initial state. What can you say about the overall change in the system's internal energy, ΔU?

The area gives you the work done by the gas. ΔW:
https://www.ux1.eiu.edu/~cfadd/1150/14Thermo/Images/Diag10.gif
If you are dealing with n moles of an ideal gas you can use PV = nRT to get the value of V at each vertex and then derive a formula for ΔW in terms of the P's, T's, n and R.

Then you can find ΔQ.

Make sure the signs (+ or -) of your answers match the sign-convention you are using.

Edit: poor wording corrected.
 
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  • #4
For an ideal gas, internal energy is a function only of temperature. By definition, Cv is given by $$mC_v=\left(\frac{\partial U}{\partial T}\right)_V$$But, since U is dependent only on T for an ideal gas, $$\Delta U=mC_v\Delta T$$
 
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What is heat and internal energy?

Heat is the transfer of thermal energy from one object to another due to a difference in temperature. Internal energy is the sum of all the kinetic and potential energies of the particles that make up a system.

How does heat transfer occur?

Heat can transfer through three main mechanisms: conduction, convection, and radiation. Conduction is the transfer of heat through direct contact between two objects. Convection is the transfer of heat through the movement of fluids. Radiation is the transfer of heat through electromagnetic waves.

What factors affect the change in heat and internal energy?

The change in heat and internal energy is affected by the mass, temperature, and specific heat capacity of a substance. The type of substance and the amount of time during which heat is applied also play a role in determining the change in heat and internal energy.

How is the change in heat and internal energy measured?

The change in heat is measured in joules (J) while the change in internal energy is measured in calories (cal) or joules (J). These measurements can be determined using equations such as Q=mcΔT (for heat) and ΔU=Q-W (for internal energy).

What are some real-world applications of change in heat and internal energy?

The concept of heat and internal energy is important in many fields, including thermodynamics, chemistry, and engineering. It is used in everyday activities such as cooking, heating and cooling systems, and power generation. It also plays a crucial role in understanding and predicting weather patterns and climate change.

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