Hey there! We receieved your request
Stay Tuned as we are going to contact you within 1 Hour
One of our academic counsellors will contact you within 1 working day.
Click to Chat
1800-5470-145
+91 7353221155
Use Coupon: CART20 and get 20% off on all online Study Material
Complete Your Registration (Step 2 of 2 )
Sit and relax as our customer representative will contact you within 1 business day
OTP to be sent to Change
Cp - Cv = R
where Cp = specific heat at constant pressure
Cv = specific heat at constant volume
R = universal gas constant
Consider one mole of a perfect gas enclosed in a perfectly conducting cylinder. Let the cylinder be fitted with a perfectly conducting, frictionless piston as shown in figure 19.1
Keeping the volume constant, let the temperature of the gas be increased from T to T + dT. If Cv is the specific heat of the gas at constant volume, then the heat supplied to increase the internal energy of the gas is CvdT.
Suppose that now we supply heat energy to the gas and allow the piston to move so as to keep the pressure constant. If the temperature changes from T to T + dT, then the part of the total energy supplied that is used in increasing the internal energy of the gas is equal to CydT. If the piston moves through a distance dx to keep the pressure constant, then the amount of external work done by the heat energy is
W = Force x Displacement
= Pressure x Surface area of the piston x Displacement = (P) (A) (dx) = P dV where dV = A dx is the increase in the volume of the gas.
Thus,
f Total heat supplied 1 = /Heat supplied at j + External work done i at constant pressure J Iconstant volume J
i.e., C dT = C dT + PdV ....................... (1)
' p V v 7
For a perfect gas,
PV = RT
.-. P (V + dV) = R (T+ d T) PV + PdV = RT + R dT
P dV = R dT, since PV = RT Hence eq (1) becomes
C dT = C dT + R dT
P v
or C = C + R
p ' V
or C - C = R
p V
This relation is known as Mayer's equation.
Note : For any mass m of the gas, cp - cy = r = nR where n = is the number of moles present in mass m.
Get your questions answered by the expert for free
You will get reply from our expert in sometime.
We will notify you when Our expert answers your question. To View your Question
Win Gift vouchers upto Rs 500/-
Register Yourself for a FREE Demo Class by Top IITians & Medical Experts Today !