An amount n (in moles) of a monatomic gas at initial temperature `T_(0)` is enclosed in a cylinderical vessel fitted with a ligth piston. The surrounding air has a temperature `T_(s)(gtT_(0))` . And the atmospheric pressure is `P_(a)` . Heat may be conducted between the surrounding and the gas through the bottom of the cylinder. The bottom has a surface area A, thickness x and thermal conductivity K. Assuming all change to be slow, find the distance moved by the piston in time t.

Answer

A, B

Explanation

`(Q/t)=(KA(T_8-T_0))/X`
`=(nC_pdT)/X=(KA(T_8-T_0))/X`
`implies(n5//2 RdT)/(dt)=(KA(T_8-T_0))/X`
`+gt(5nR)/2 (dT)/(dt)=(KA(T_8-T_0))/X`
`(dT)/(T_8-T_0)=(-2KAdt)/(5nRX)`
`(T_8-T_0)_(T_0)^(T)`
`(-2KAdt)/(5nRX)`
`impliesIn(T_8-T)/T_8-T_0)=(-2KAdt)/(5nRX)`
`impliesT_8-T=(T-8-T_0)e^(-2KAt)//(5nRX)`
`T=(T_8-T_0)e(-2KAt)/(5nRX)`
`implies (P^aAl)/(nR)=T-T_0`
(T_8-T_0)(T_8-T_0)e^(-2KAt)/(5nRX)`
`(T_8-T_0)((1-e^(-2KAt)/(5nRX))`
`=(nR)/(P_aA)xx(T_8-T_0)((1-e^(-2KAt)/(5nRX))`.