Two moles of an ideal monoatomic gas undergoes a process `VT =` constant. If temperature of the gas is increased by `DeltaT = 300K`, then the ratio `((DeltaU)/(DeltaQ))` is

Options

A. 2
B. 3
C. 4
D. 6

Answer

B

Explanation

Given, `VT =` constant
`PV^(2) =` constant
Polytropic constant, `x = 2`
`:.` Molar heat capcity,
`C = C_(v) + (R )/(1 - x)`
`= (3R)/(2) + (R )/(1 - 2)`
`= (R )/(2)`
`:. DeltaQ = nCdeltaT = 2xx (R )/(2) xx 300 = 300R`
`DeltaU = nC_(v)DeltaT = 2 xx (3R)/(2) xx 300 = 900R`
`:. (DeltaU)/(DeltaQ) = (900R)/(300R) = 3`