# What is the molar heat capacity of an ideal gas at constant pressure and volume?

• Banyans
In summary: Also, pay attention to units.5/2R?Yes, that is correct. In summary, the molar heat capacity at constant pressure C_p,m for the ideal gas is 29.25 J/K mole and the molar heat capacity at constant volume C_v,m is 20.93 J/K mole. Since C_v,m is equal to 3/2R which is the value for a monatomic gas, it can be concluded that the gas in question is monatomic.
Banyans

## Homework Statement

117 J of energy is supplied as heat to 2.00 moles of an ideal gas at constant
pressure, the temperature rises by 2.00 K. Calculate the molar heat capacity at
constant pressure C_p,m and the molar heat capacity at constant volume C_v,m
for the gas. Is the gas monatomic or diatomic?

PV = nRT
ΔQ = n Cp ΔT

## The Attempt at a Solution

ΔQ = 117 J
n = 2 moles
ΔT = 2 K

ΔQ = n Cp ΔT = n αR ΔT
Cp = ΔQ/ (nΔT) = 29.25 J/K mole
Cp/R = 3.52

For ideal gases equation of state is
PV = nRT,
and work performed by the gas in isobaric process is
dA = PdV = nRdT,
which means Cv = Cp - R = 2.52 R.

But I have no idea how to relate this information to work out if its diatomic or monatomic.

What is Cp for an ideal monoatomic gas?

Hello Banyans,

Hard to give a hint here without spoiling the exercise. Don't the values of ##{7\over 2}## and ##{5\over 2}## ring a bell ? What would they be for an ideal monatomic gas ?

mfb said:
What is Cp for an ideal monoatomic gas?
5/2R?

So would I proceed in the following way?

Cp=29.25

Cp=Cv+nR
29.25=Cv+2(8.31451)

so

Cv=12.621

So there fore its a monoatomic gas? since Cv=3/2R?

Banyans said:
5/2R?
That is Cp for a monoatomic gas, right. Does that match the result you got for the unknown gas?
Banyans said:
Cp=Cv+nR
That formula is not right. Use specific heat capacities or use total heat capacities, but do so in a consistent way.

## What is heat capacity?

Heat capacity is the amount of heat required to raise the temperature of a substance by one degree.

## What is the difference between specific heat capacity and molar heat capacity?

Specific heat capacity is the amount of heat required to raise the temperature of one gram of a substance by one degree, while molar heat capacity is the amount of heat required to raise the temperature of one mole of a substance by one degree.

## How is heat capacity measured?

Heat capacity is typically measured using a calorimeter, which is a device that measures the change in temperature of a substance when heat is added or removed.

## What factors affect heat capacity?

The main factors that affect heat capacity are the type of substance, its mass, and its temperature. Different substances have different heat capacities, and substances with higher mass typically have higher heat capacities. Additionally, as the temperature of a substance increases, its heat capacity may change.

## Why is heat capacity important in science?

Heat capacity is important in science because it helps us understand how different substances respond to changes in temperature. It is also a crucial factor in many practical applications, such as designing heating and cooling systems or understanding the behavior of materials in different environments.

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