Advertisements
Advertisements
प्रश्न
Derive Meyer’s relation for an ideal gas.
Advertisements
उत्तर
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
संबंधित प्रश्न
Heat energy is supplied at a constant rate to 100g of ice at 0 °C. The ice is converted into water at 0° C in 2 minutes. How much time will be required to raise the temperature of water from 0 °C to 20 °C? [Given: sp. heat capacity of water = 4.2 J g-1 °C-1, sp. latent heat of ice = 336 J g-1].
What do you mean by the following statement?
The heat capacity of a body is 50 JK-1?
Give three reasons for the increase of green house gases.
How will rise in sea level affect population in coastal countries?
In Regnault's apparatus for measuring specific heat capacity of a solid, there is an inlet and an outlet in the steam chamber. The inlet is near the top and the outlet is near the bottom. Why is it better than the opposite choice where the inlet is near the bottom and the outlet is near the top?
Indian style of cooling drinking water is to keep it in a pitcher having porous walls. Water comes to the outer surface very slowly and evaporates. Most of energy needed for evaporation is taken from the water itself and the water is cooled down. Assume that a pitcher contains 10 kg of water and 0.2 g of water comes out per second. Assuming no backward heat transfer from the atmosphere to the water, calculate the time in which the temperature decrease by 5°C. Specific heat capacity of water = 4200 J kg−1 °C−1 and latent heat of vaporization of water = 2.27 × 106 J kg−1.
Fill in the following blank using suitable word:
SI unit of heat is .........
Explain, why does a wise farmer water his fields, if forecast is forst?
Two metals A and B have specific heat capacities in the ratio 2 : 3. If they are supplied the same amount of heat then
Which metal piece will show a greater rise in temperature given their masses is the same?
