Question 1: Thermodynamics & KTG

Question

A cylinder of mass $1 \mathrm{~kg}$ is given heat of $20000 \mathrm{~J}$ at atmospheric pressure. If initially temperature of cylinder is $20^{\circ} \mathrm{C}$, find
(A) The final temperature of the cylinder;
(B) The work done by the cylinder;
(C) The change in internal energy of the cylinder.
Given :
The specific heat of cylinder
$=400 \mathrm{~J} \mathrm{~kg}^{-1 \circ} \mathrm{C}^{-1}$
Coefficient of volume expansion
$=9 	imes 10^{-5}{ }^{\circ} \mathrm{C}^{-1} 	ext {; }$
Atmospheric pressure $=10^{5} \mathrm{~N} / \mathrm{m}^{2}$ Density of cylinder $=9000 \mathrm{~kg} / \mathrm{m}^{3}$ )

Accepted Answer

(A) Heat supplied to the cylinder is used up in if raising temperature of cylinder $=m s \Delta \mathrm{T}$
(i) $\mathrm{Q}_{1}=m s \Delta \mathrm{T}=1 	imes 400(\mathrm{~T}-20) 	ext {...(i) }$
S = 400 J kg$^{-10}$C$^{-1}$
(ii) doing work $=\mathrm{P}_{	ext {atom }}\left(\mathrm{V}_{2}-\mathrm{V}_{1}ight)$
Work done $=\mathrm{P}_{\mathrm{atm}}\left(\mathrm{V}_{2}-\mathrm{V}_{1}ight)$
$\mathrm{Q}_{2}=10^{5} 	imes\left(\mathrm{V}_{1} \gamma \Delta \mathrm{T}ight)$
$\mathrm{Q}_{2}=10^{5} 	imes \frac{	ext { mass }}{	ext { density }} 	imes \gamma(\mathrm{T}-20)$
$\mathrm{Q}_{2}=10^{5} 	imes \frac{1}{900} 	imes 9 	imes 10^{-5} 	imes(\mathrm{T}-20)$
$\mathrm{Q}_{2}=0.001(\mathrm{~T}-20)$ ...... (ii)
$	herefore \quad \mathrm{Q}_{1}+\mathrm{Q}_{2}=\mathrm{Q}$ Heat supplied.
(Given $\mathrm{Q}=20000 \mathrm{~J}$ )
400.$(T-20)+0.001(T-20)=20000$
$400.001(\mathrm{~T}-20)=2000$
$\mathrm{T}-20=\frac{20000}{400.001}=50$ (approx)
$\mathrm{T}=50+20=70^{\circ} \mathrm{C}$ ...... (iii)
(B) Workdone by cylinder
$\begin{aligned}
\mathrm{W} & =\mathrm{Q}_{2}=0.001(70-2 a) \
& =0.001(50) \
\mathrm{W} & =0.05 \mathrm{~J} .\end{aligned}$
(C) Change in internal energy
$\begin{aligned}
\Delta \mathrm{U} & =20000-0.05 \
& =19999.95 \mathrm{~J}=1.9 	imes 10^{4} \mathrm{~J}
\end{aligned}$

Answer

$(\mathrm{A}) 70^{\circ} \mathrm{C}$, (B) $0.05 \mathrm{~J}$ (C) $\Delta \mathrm{U}=1.9 	imes 10^{4} \mathrm{~J}$

Answer

$(\mathrm{A}) 70^{\circ} \mathrm{C}$, (B) $0.05 \mathrm{~J}$ (C) $\Delta \mathrm{U}=2.9 	imes 10^{4} \mathrm{~J}$

Answer

$(\mathrm{A}) 60^{\circ} \mathrm{C}$, (B) $0.05 \mathrm{~J}$ (C) $\Delta \mathrm{U}=1.9 	imes 10^{4} \mathrm{~J}$

Answer

$(\mathrm{A}) 70^{\circ} \mathrm{C}$, (B) $0.07 \mathrm{~J}$ (C) $\Delta \mathrm{U}=1.9 	imes 10^{4} \mathrm{~J}$

Thermodynamics & KTG

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