Advertisements
Advertisements
Question
Derive Meyer’s relation for an ideal gas.
Advertisements
Solution
Meyer’s relation: Consider p mole of an ideal gas in a container with volume V, pressure P and temperature T.
When the gas is heated at constant volume the temperature increases by dT. As no work is done by the gas, the heat that flows into the system will increase only the internal energy. Let the change in internal energy be dU.
If Cv is the molar specific heat capacity at constant volume, from the equation.
`"C"_"v" = 1/µ "dU"/"dT"` ..........(1)
dU = µCvdT .........(2)
Suppose the gas is heated at constant pressure so that the temperature increases by dT. If ‘Q’ is the heat supplied in this process and ‘dV’ the change in volume of the gas.
Q = µCPdT …............(3)
If W is the work done by the gas in this process, then
W = PdV …................(4)
But from the first law of thermodynamics,
Q = dU + W …...............(5)
Substituting equations (2), (3) and (4) in (5), we get,
µCpdT = µCvdT + PdV
For mole of an ideal gas, the equation of state is given by
PV = µRT ⇒ PdV + VdP = µRdT
Since the pressure is constant, dP = 0
∴ CpdT = CvdT + RdT
∴ CP = Cv +R (or) Cp − Cv = R ......(6)
This relation is called Meyer’s relation It implies that the molar specific heat capacity of an ideal gas at constant pressure is greater than molar specific heat capacity at constant volume. The relation shows that specific heat at constant pressure (sp) is always greater than specific heat at constant volume (sv).
APPEARS IN
RELATED QUESTIONS
A liquid X has the maximum specific heat capacity and is used as a coolant in Car Radiators. Name the liquid X.
A solid metal weighing 150 g melts at its melting point of 800 °C by providing heat at the rate of 100 W. The time taken for it to completely melt at the same temperature is 4 min. What is the specific latent heat of fusion of the metal?
650 J of heat is required to raise the temp. of 0.25 kg of lead from 15°C to 35°C. Calculate the Sp. heat capacity of lead.
If, in a central heating system, steam enters a radiation pipe at 100°C and water leaves the radiation pipe at 100°C, can this radiation pipe heat a room? Give an explanation for your answer.
A. hot solid of mass 60 g at 100°C is placed in 150 g of water at 20° C. The final steady temperature recorded is 25°C. Calculate the specific heat capacity of the solid. [Specific heat capacity of water = 4200 J kg-1 °C-1]
Decide the unit for specific heat capacity.
Explain why the specific heat capacity at constant pressure is greater than the specific heat capacity at constant volume.
A diatomic gas undergoes adiabatic change. Its pressure 'P' and temperature 'T' are related as p ∝ Tx, where x is ______.
Two metals A and B have specific heat capacities in the ratio 2:3. If they are supplied same amount of heat then
Which metal piece will have greater mass if the rise in temperature is the same for both metals?
