Molar specific heat of an ideal gas

In summary, the question asks for the energy transferred by heat in a two-step warming process of a diatomic ideal gas. The first step is at constant pressure, where the pressure triples and the volume doubles. The second step is at constant volume, where the pressure changes from Po to 3Po and the volume changes from Vo to 2Vo. To calculate the energy transferred by heat, we use the equations Q = nCpΔT for constant pressure and Q = nCvΔT for constant volume. We also use the ideal gas formula PV = nRT to substitute for n in the equations. By calculating the change in temperature for each step, we can then add Q1 + Q2 to get the total
  • #1
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Homework Statement



A sample of a diatomic ideal gas has pressure P and volume V. When the gas is warmed, it's pressure triples and the it's volume doubles. This warming process includes two steps, the first at constant pressure and the second at constant volume. Determine the energy transferred by heat.


Homework Equations



Q = nCvΔT(constant volume)
Q = nCpΔT(constant pressure)

The Attempt at a Solution


Since it occurs in two phases, my thought was to add Q1 + Q2. Q1 at constant pressure and Q2 at constant volume i.e.

(n x 7/2R x ΔT) +(n x 5/2R x ΔT)
nRΔT is common thus;
nRΔT(7/2 + 5/2)
= 6nRΔT. or 6PV (since PV = nRT)

But my answer is wrong..and I'm NOT sure if my conclusion that nRΔT = nRT is true..
Any help is very much appreciated..thanks
 
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  • #2
Hi fiziks09! :smile:

Did you notice that you did not use the information that the pressure triples and the volume doubles?

Consider also that you don't know ΔT of each process step. They will not be the same.
 
  • #3
thanks..
i noticed that..but the thing is i don't know where to fit that information. I also can't think of any other equations relevant to the question aside from the ones in put up there
 
  • #4
What about the ideal gas formula: PV=nRT?
 
  • #5
Okay..i have been on this quite a while now..
i substituted n = PV/RT in the equations for both constant pressure and constant volume..
i then used p = 3P and v = 2V.. but it didn't work..

Also..how about the initial states of the gas, i couldn't figure out where to fit them in ?.
 
  • #6
What did not work?

The initial state of the gasses would be P=Po, and V=Vo.

Step 1 is constant pressure, so V changes from Vo to 2Vo at P=Po.
Furthermore Q = nCpΔT. Calculate ΔT from P and V.

Step 2 is constant volume, so P changes from Po to 3Po at V=2Vo.
Furthermore Q = nCvΔT. Calculate ΔT from P and V.
 

1. What is the definition of molar specific heat of an ideal gas?

The molar specific heat of an ideal gas is the amount of heat required to raise the temperature of one mole of the gas by one degree Celsius at constant pressure.

2. How is molar specific heat of an ideal gas different from specific heat?

Molar specific heat is the amount of heat required for a specific amount of substance (one mole) while specific heat is the amount of heat required for a specific mass of substance (usually one gram).

3. What is the equation for calculating molar specific heat of an ideal gas?

The equation is: Cp = (3/2)R, where Cp is the molar specific heat at constant pressure and R is the gas constant.

4. How does temperature affect molar specific heat of an ideal gas?

In an ideal gas, molar specific heat is independent of temperature as long as the gas remains in the ideal state. This means that it will have the same value at any temperature.

5. Can the molar specific heat of an ideal gas change?

In an ideal gas, the molar specific heat at constant pressure remains constant. However, at very high temperatures or pressures, the gas may deviate from ideal behavior and the molar specific heat may change slightly.

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