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.
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##?
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 ).
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.
utkarshakash said:Cp-Cv = R
The formula for calculating Cp of a gas at STP is Cp = (nR)/2, where n is the number of moles of the gas and R is the gas constant (8.314 J/mol*K).
The value of Cp for an ideal gas at STP is 20.79 J/mol*K.
To convert 4.48 L to moles, you will need to use the ideal gas law equation: PV = nRT. Rearrange this equation to solve for n, where n is the number of moles. Then, plug in the given values of P (1 atm), V (4.48 L), T (15°C converted to Kelvin), and R (8.314 J/mol*K) to solve for n.
Yes, this formula can be used to calculate Cp for any gas at STP as long as you have the number of moles of the gas and the gas constant. However, it is important to note that this formula assumes an ideal gas behavior, so it may not be accurate for real gases.
Cp is an important thermodynamic property of a gas and is used in various calculations, such as determining the heat capacity of a system or the change in enthalpy of a reaction. It is also used in the design and operation of industrial processes involving gases. Knowing the value of Cp at STP can provide valuable information for these applications.