AP EAPCET 19-Aug-2021 Shift 1 Paper

Given, initial temperature T1=30∘C
=303K
Change in radius, ∆r=0.08mm
Internal diameter of cylinder dc=15cm
∴ Internal radius of cylinder, rc=7.5×10−2m
Radius of piston, rp=(7.5−0.008)×10−2m
=7.492×10−2m
Linear expansion of cylinder αC and piston αp are 1.2×10−5∕‌∘C and 1.6×10−5∕‌∘C .
Let, ∆rC and ∆rp is increase in radius of cylinder and piston respectively, for fully filled piston in cylinder.
By using equation of linear expansion,
r=r0(1+α∆T)
∴‌‌∆rC=rCαC∆T , for cylinder
New radius will be rC′=rC+∆rC
=rC+rCαC∆T=rC(1+αC∆T)
=7.5×10−2[1+1.2×10−5(T−303)]
Similarly, new radius of piston,
rp′=7.492×10−2[1+1.6×10−5(T−303)]
Now, for fully fitted piston, rC=rp
7.5×10−2[1+1.2×10−5(T−303)]
=7.492×10−2[1+1.6×10−5(T−303)]
⇒‌‌1.0011+1.2013×10−5(T−303)
=1+1.6×10−5(T−303)
⇒1.1×10−3=(T−303)×10−5(1.6−1.2013)
=(T−303)×10−5×0.3987
⇒T−303=275
⇒‌‌T=578K=305∘C