When 229.0 J of energy is supplied as heat to 3.00 mol of Ar(g) at constant pressure the temperature of the sample increases by 2.55 K. Assuming that in the experiment the gas behaves as an ideal gas, calculate the molar heat capacities at constant volume and at constant pressure of Ar(g).

The molar heat capacity at constant volume is 21.62 JK⁻¹mol⁻¹

The molar heat capacity at constant pressure is 29.93 JK⁻¹mol⁻¹

Explanation:

We can calculate the molar heat capacity at constant pressure from

Where is the molar heat capacity at constant pressure

is the heat capacity at constant pressure

and is the number of moles

Also is given by

Hence,

becomes

From the question,

= 229.0 J

= 3.00 mol

= 2.55 K

Hence,

becomes

29.93 JK⁻¹mol⁻¹

This is the molar heat capacity at constant pressure

For, the molar heat capacity at constant volume,

From the formula

Where is the molar heat capacity at constant volume

and is the gas constant ( = 8.314 JK⁻¹mol⁻¹)

Then,

21.62 JK⁻¹mol⁻¹

This is the molar heat capacity at constant volume