Equation for molar specific heat

In summary, the molar specific heat at constant volume of a mixture of n_1 moles of a monatomic gas and n_2 moles of a diatomic gas can be derived using the equation Q = C_v(n_1+n_2)*delta(T). By setting this equal to the equation Q = 3/2nR*delta(T), C_v can be solved for. However, simply using C_v = 3/2R is incorrect, as it does not take into account the different specific heat values for diatomic gases (5/2R). With this information, the correct equation for the molar specific heat of the mixture is Q = (n_1+n_2)*(5/2
  • #1
Metalsonic75
29
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n_1 moles of a monatomic gas and n_2 moles of a diatomic gas are mixed together in a container. Derive an expression for the molar specific heat at constant volume of the mixture. Expression must be in terms of n_1, n_2, and the gas constant R.

I know that the molar specific heat of the entire mixture is Q = C_v(n_1+n_2)*delta(T). and my physics professor told me that I can use the equation Q = 3/2nR*delta(T) and set it equal to C_v(n_1+n_2)*delta(T) and somehow use that to solve for something, but I'm not sure what I can solve for. I keep getting C_v = 3/2R, but when I plug that in, the equation doesn't work ( 3/2R(n_1+n_2) is incorrect ). I would appreciate some help. Thanks
 
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  • #2
The molar specific heat of a diatomic gas is 5/2R. Does this help?
 
  • #3
Got it! Thanks!
 

What is the equation for molar specific heat?

The equation for molar specific heat is c = q/(nΔT), where c is the molar specific heat, q is the heat absorbed or released, n is the number of moles of the substance, and ΔT is the change in temperature.

What are the units for molar specific heat?

The units for molar specific heat are J/mol·K or cal/mol·K. This means joules per mole per Kelvin or calories per mole per Kelvin.

How is molar specific heat different from specific heat?

Molar specific heat is the amount of heat needed to raise the temperature of one mole of a substance by one degree Kelvin, while specific heat is the amount of heat needed to raise the temperature of one gram of a substance by one degree Celsius.

What factors can affect the molar specific heat of a substance?

The molar specific heat of a substance can be affected by its molecular structure, temperature, and phase (solid, liquid, or gas). Other factors, such as pressure, can also have an impact.

Can the molar specific heat of a substance change?

Yes, the molar specific heat of a substance can change if there is a change in its molecular structure or if there is a change in phase. It can also vary with temperature and pressure.

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