A cylinder of mass 1kg is given heat of 20,000J at atmospheric pressure. If initially the temperature of cylinder is `20^@C`, find
(a) final temperature of the cylinder.
(b) work done by the cylinder.
(c) change in internal energy of the cylinder
(Given that specific heat of cylinder=`400Jkg^-1^@C^-1,` Atmospheric pressure= `10^5N//m^2` and Density of cylinder=`9000kg//m^3`)

Answer

A, C, D

Explanation

(a) Heat supplied to the cylinder =Energy used to raise
the temperature of cylinder+Energy used for work
done by the cylinder.
Energy used to raise the temperature =`mcDeltaT`
`=1xx400xx(T-20)….(i)`
where `T^@C` is the final temperature of the cylider.
Energy used for work done
`=P_(atm)(V_2-V_1)=10^5(V_2-V_1)....(ii)`
The final volume `V_2=V_1[1+gamma(T-20)]`
`rArrV_2-V_1=V_1gamma (T-20)....(iii)`
From (ii) and (iii),
`Energy used by work done=10^5V_1gamma(T-20)`
`=10^5xx1/9000xx9xx10^-5(T-20) [:'V_1=m/d=1/9000]`
`=0.001(T-20).....(iv)`
`:.` Heat supplied to the cylinder
` =400(T-20)+0.001(T-20)`
`20,000=400.001(T-20)`
`rArrT=69.99^@C~~70^@C`
(b) `work done =0.001(69.99-20)=0.0499J`
(c) `Change in internal energy=20,000-0.0499=19999.95J.`