A uniform tube of volume V contains an ideal monatomic gas at a uniform pressure `P` the temperature of the gas varies linearly along te length of the tube ad T and 2 T are the temperature at the ends.

Options

A. The number of moles of the gas in the tube is `(PV)/(RT)l n2`
B. The number of moles of the gas in the tube is `(PV)/(RT) l n4`
C. The internal energy of the gas in the tube is `(3//2)PV`
D. The internal energy of the gas in the tube is `(3//2)nRT`.

Answer

A, C

Explanation

`T^(')=T+(T)/(l)ximpliesdT^(')=(T)/(l)dx`
`n=intdn=int(Padx)/(RT^('))=int_(T)^(2T)(PV)/(RT)(dT^('))/(T^('))`
`n=(PV)/(RT)l n2`
`U=(f)/(2)PV`