Calculate Cp of a Gas at STP - 4.48 L & 15°C

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To calculate the heat capacity at constant pressure (Cp) of a gas at STP, given that 4.48 L requires 12 cal to raise the temperature by 15°C at constant volume, the relationship between Cp and Cv is essential. The equation ΔU = nCvΔT can be used to find Cv, but the challenge lies in determining Cp without knowing the gas's degrees of freedom. The relation Cp - Cv = R, where R is the gas constant (1.9872041 cal/K/mole), is applicable, but the specific nature of the gas must be identified to accurately calculate Cv. Once Cv is determined, Cp can be derived using the established equations. Understanding these relationships is crucial for solving the problem effectively.
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Homework Statement


4.48 L of an ideal gas at STP requires 12 cal to raise the temperature by 15°C at constant volume. The Cp of the gas is (in cal)?


The Attempt at a Solution



ΔU = nCvΔT
I can find out C_v from above equation but how to get C_p? I assume it would be wrong to use this equation ΔQ=nCpΔT as the process is carried out at constant volume and not pressure.
 
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utkarshakash said:

Homework Statement


4.48 L of an ideal gas at STP requires 12 cal to raise the temperature by 15°C at constant volume. The Cp of the gas is (in cal)?


The Attempt at a Solution



ΔU = nCvΔT
I can find out C_v from above equation but how to get C_p? I assume it would be wrong to use this equation ΔQ=nCpΔT as the process is carried out at constant volume and not pressure.

You said you can calculate ##C_v## (and btw, it comes out to be a nice integer, keep everything in cal). Do you know of a relation between ##C_v## and ##C_p##?
 
Pranav-Arora said:
You said you can calculate ##C_v## (and btw, it comes out to be a nice integer, keep everything in cal). Do you know of a relation between ##C_v## and ##C_p##?

I did use that relation earlier but since the question is an integer type(you know what they mean,don't you?) it won't give me an integral answer(rounding off the digits still gives an answer beyond the range ).
 
utkarshakash said:
I did use that relation earlier but since the question is an integer type(you know what they mean,don't you?) it won't give me an integral answer(rounding off the digits still gives an answer beyond the range ).

May I know which relation did you use?

I should have said to use a relation between ##C_v## and degrees of freedom. You should be able to calculate ##C_p## once you have the degrees of freedom.
 
Pranav-Arora said:
May I know which relation did you use?

I should have said to use a relation between ##C_v## and degrees of freedom. You should be able to calculate ##C_p## once you have the degrees of freedom.

Cp-Cv = R

The question does not state the nature of gas. So degrees of freedom is not known.
 
utkarshakash said:
Cp-Cv = R

So what did you plug in for Cv? Note that it should be in cal. And what is the value of R in calorie units?
 
R = 1.9872041 cal/K/mole
and Cv you can calculate from ΔU = nCvΔT.
the put Cp-Cv = R
 

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