A water tank is completely filled with liquid water at 20 degree Celcius. The tank material is such that it can withsatand tension caused by a volume expansion of 2%. Determine the max temperature rise in Celcius degress allowed without jeopardizing safety. Neglet the effect of pressure change.

Respuesta :

Answer:[tex]73.05[/tex]

Explanation:

Given

Initial Water Temperature is [tex]20^{\circ}[/tex]

and volume expansion is 2%

Also we know that water volume expansion coefficient is [tex]0.377\times 10^{-3}/K[/tex]

[tex]V=V_0(1+\gamma \Delta T)[/tex]

[tex]\frac{\Delta V}{V}=\gamma \Delta T[/tex]

[tex]0.377\times 10^{-3}\times \Delta T=0.02[/tex]

[tex]\Delta T=\frac{0.02}{0.377\times 10^{-3}}[/tex]

[tex]\Delta =53.05[/tex]

[tex]T_2-20=53.05[/tex]

[tex]T_2=73.05 ^{\circ}[/tex]

Answer:

The max temperature rise in Celsius degrees allowed without jeopardizing safety is [tex]$T_{2}=73.05^{\circ}$[/tex].

Explanation:

The volume expansion of tank is [tex]$2 \%$[/tex].

At [tex]20[/tex] degree Celsius.

[tex]$V=V_{0}(1+\gamma \Delta T)$[/tex]

[tex]$\frac{\Delta V}{V}=\gamma \Delta T$[/tex]

Water volume expansion coefficient : [tex]$0.377 \times 10^{-3} / K$[/tex]

[tex]$0.377 \times 10^{-3} \times \Delta T=0.02$[/tex]

[tex]$\Delta T=\frac{0.02}{0.377 \times 10^{-3}}$[/tex]

[tex]$\Delta=53.05$[/tex]

The temperature is,

[tex]$T_{2}-20=53.05$[/tex]

[tex]$T_{2}=73.05^{\circ}$[/tex]

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