Given, initial temperature
T1=30∘C =303KChange in radius,
∆r=0.08mmInternal diameter of cylinder
dc=15cm ∴ Internal radius of cylinder,
rc=7.5×10−2mRadius of piston,
rp=(7.5−0.008)×10−2m =7.492×10−2mLinear 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
