00:01
Let's solve the given question.
00:02
In this question we have given that is cv is greater than the cv when heat is added.
00:10
When heat is added to a gas at constant volume, at constant volume qv is equals to cv dt which is equals to del of u plus w for v is equals to constant w is equals to zero.
00:44
This implies q of v is equals to, let it call equation first, so equation first become cv dt which is equals to del of u.
00:54
So when heat is, let it call equation second, so when heat is added to a gas, to a gas at constant pressure qp is equals to cp dt that is equals to del u plus w.
01:30
So for p constant, so p as constant, this implies w is equals to p dot dv or we can say q of p is equals to cp dt is equals to del u plus p dot dv.
01:53
Now when a gas is heated, we can say that when a gas is heated at constant volume, at constant volume no external work, no external work is done and heat supply and heat supplied is consumed, is consumed only in increasing, only in increasing the internal, internal energy that is del of u.
03:04
But if the gas is heated, but if the gas is heated at constant pressure, at constant pressure heat supplied, heat supplied is consumed, is consumed in increasing, increasing internal energy, internal energy that is del of u and work done is equals to p dot dv.
03:55
Since del of u is equals to function of temperature and for same temperature rise, for say temperature rise cp is greater than cv.
04:19
So we can say cp minus cv is equals to r.
04:23
As we have to prove this that is cp minus cv is equals to r.
04:29
So for this as proof is that is enthalpy, enthalpy h is given by u plus pv.
04:43
So pv is equals to mrt...