A gas is enclosed in a cylindrical vessel fitted with a frictionless piston.the gas is slowly heated for some time. During the process, 10 J of heat is supplied and the piston is found to move out 10cm. Find the increase in the internal energy of the gas, the area of cross section of the cylinder=`4 cm^(2)` and the atmospheric pressure `=100 kPa.`

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))`.