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 have CV = 5 2 R and CP = 7 2 R. Use any variable or symbol stated above as necessary.)

Answer 1

13.5PV

Step-by-step explanation:

Through the first process, the change in internal energy is

ΔE=
`(5)/(2)nR\delta T`

we know that

nRΔT= 2PV-PV= PV

so ΔE= 5/2×PV

work done = PΔV= PV

the heat is Q= 5/2×PV+ PV= 7/2×PV

through the second process, work done is zero

So, Q = ΔE =
`(5)/(2)nR\delta T`

⇒ ΔE= 5/2( 6PV- 2PV) = 10PV

therefore total heat energy transferred to gas = 10PV+ 3.5PV = 13.5PV