Question

A sample of a diatomic ideal gas has pressure P and volume V. When the gas is warmed, its pressure triples and its volume doubles. This warming process includes two steps, the first at constant pressure and the second at constant volume. Determine the amount of energy transferred to the gas by heat. (Here we define a "diatomic ideal gas" to haveCV =52RandCP =72R.Use any variable or symbol stated above as necessary.)

Answer 1

Amount of Energy transferred =8.5PV=8.5PV

Answer 2

Amount of Energy transferred
`=8.5PV`

Step-by-step explanation:

Given:

Initial volume=V

Initial pressure=P

Final volume=2V

Final pressure=3P

Now w know that the Energy transferred in constant pressure pressure is given by

`E_1=nc_pdT\\\\E_1=n*(7R)/(2)dT\\E_1=3.5(nRdT)\\E_1=3.5(V(2P-P))\\E_1=3.5PV`

Now the Energy transferred in constant volume process is given by

`E_2=nc_vdT\\\\E_2=n*(5R)/(2)dT\\E_1=2.5(nRdT)\\E_1=2.5(V(3V-V))\\E_1=5PV`

The total Energy transferred is given by

`E_(total)=E_1+E_2\\E{total}=3.5PV+5PV\\=8.5PV`