An ideal gas has a specific heat at constant pressure `C_p=(5R)/(2)`. The gas is kept in a closed vessel of volume `V_0` at temperature `T_0` and pressure `p_0`. An amount fo `10p_0V_0` of heat is supplied to the gas.
(a) Calculate the final pressure and temperature of the gas.
(b) Show the process on p-V diagram.

Answer

A, B, C

Explanation

(a) First law of thermodynamics for the given process form state 1 to state 2
`Q_(12)-W_(12)=U_2-U_1`
Here, `Q_(12)=+10p_0V_0` joule
`W_(12)=0` (Volume remains constant)
`U_2-U_1=nC_V(T_2-T_1)`
`nC_V(T_2-T_1)=10p_0V_0`
For an ideal gas,
`p_0V_0=nRT_0`
and `C_p-C_V=R`
`:.` `C_V=C_p-R`
`=(5R)/(2)-R=(3R)/(2)`
`:.` `n((3R)/(2))(T_2-T_0)=10nRT_0`
`T_2=(23)/(3)T_0`
As `ppropT` for constant volume
`p_2=(23)/(3)p_0`
(b)