Question

a monatomic ideal gas undergoes a process in which the ratio of p to v at any instant is constant and equal to 1 . what is the molar heat capacity if the gas

Answer 1

Answer:

Given is $\frac{P}{V} =1$

P=V------(1)

From I law

dq=CvdT+pdV-------(2)

For 1 mole of an ideal gas pV=RT

differentiate this equation

pdV+Vdp=RdT

From equation 1

2pdV=RdT

pdV=$\frac{RdT}{2}$

substitute these value in equagtion 2 we get

dq=CvdT+$\frac{RdT}{2}$

$\frac{dq}{dT} =C_{V} +\frac{R}{2}$

                           =$\frac{3}{2} R+\frac{R}{2}$

                           =$\frac{4R}{2}$

                           =2R

So here $\frac{dq}{dT}$ is the molar heat capacity.