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I'm trying to show a formula for an ideal gas, but I don't get the right results.

For an ideal gas PV = nRT where n is the number of momles. Show that the heat transferred in an infinitesimal quasistatic process of an ideal gas can be written as

[tex]dQ = \frac{C_V}{nR}VdP + \frac{C_P}{nR}PdV[/tex]

[tex]

dU = dQ + dW

[/tex]

[tex]

C_P = C_V + R

[/tex]

[tex]

dU = nC_VdT

[/tex]

[tex]

dW = -PdV

[/tex]

I differented the formula for the ideal gas PV = nRT so it becomes

PdV + VdP = nRdT

[tex]

dT = \frac{PdV + VdP}{nR}

[/tex]

[tex]

dU = C_V\frac{PdV + VdP}{R}

[/tex]

[tex]

dQ = C_V\frac{PdV + VdP}{R} + PdV = \left(\frac{C_V}{R} + 1\right)PdV + \frac{C_V}{R}VdP = \frac{C_P}{R}PdV + \frac{C_V}{R}VdP

[/tex]

What have I done wrong? There is no dependens on n in my final equation.

I know there should be bars on dW and dQ but i didn't got it to work in latex :/

## Homework Statement

For an ideal gas PV = nRT where n is the number of momles. Show that the heat transferred in an infinitesimal quasistatic process of an ideal gas can be written as

[tex]dQ = \frac{C_V}{nR}VdP + \frac{C_P}{nR}PdV[/tex]

## Homework Equations

[tex]

dU = dQ + dW

[/tex]

[tex]

C_P = C_V + R

[/tex]

[tex]

dU = nC_VdT

[/tex]

[tex]

dW = -PdV

[/tex]

## The Attempt at a Solution

I differented the formula for the ideal gas PV = nRT so it becomes

PdV + VdP = nRdT

[tex]

dT = \frac{PdV + VdP}{nR}

[/tex]

[tex]

dU = C_V\frac{PdV + VdP}{R}

[/tex]

[tex]

dQ = C_V\frac{PdV + VdP}{R} + PdV = \left(\frac{C_V}{R} + 1\right)PdV + \frac{C_V}{R}VdP = \frac{C_P}{R}PdV + \frac{C_V}{R}VdP

[/tex]

What have I done wrong? There is no dependens on n in my final equation.

I know there should be bars on dW and dQ but i didn't got it to work in latex :/

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