Answer:
108507.02596 Pa
42.42 cm
Explanation:
F = Force
m = Mass of piston = 23 kg
[tex]T_1[/tex] = Initial temperature = 307°C
[tex]T_2[/tex] = Final temperature = 13°C
[tex]P_o[/tex] = Outside pressure
[tex]P_i[/tex] = Pressure inside cylinder
A = Area of pistion
h = Height of piston
Change in pressure is given by
[tex]\Delta P=\frac{F}{A}\\\Rightarrow \Delta P=\frac{mg}{\pi r^2}\\\Rightarrow \Delta P=\frac{23\times 9.81}{\pi 0.1^2}\\\Rightarrow \Delta P=7182.02596\ Pa[/tex]
[tex]P_i-P_o=\Delta P\\\Rightarrow P_i=\Delta P+P_0\\\Rightarrow P_i=7182.02596+101325\\\Rightarrow P_i=108507.02596\ Pa[/tex]
Gas pressure inside the cylinder is 108507.02596 Pa
From ideal gas law we have the relation
[tex]\frac{V_1}{T_1}=\frac{V_2}{T_2}\\\Rightarrow \frac{Ah_1}{T_1}=\frac{Ah_2}{T_2}\\\Rightarrow \frac{h_1}{T_1}=\frac{h_2}{T_2}\\\Rightarrow h_2=\frac{h_1}{T_1}\times T_2\\\Rightarrow h_2=\frac{0.86}{307+273.15}\times (13+273.15)\\\Rightarrow h_2=0.42418\ m=42.42\ cm[/tex]
The height of the piston at 13°C will by 42.42 cm
(a) The gauge pressure inside the cylinder is 108,500 Pa.
(b) The height of the piston when the temperature is lowered to 13°C is 42.4 cm.
The change in the pressure of the gas inside the cylinder is calculated as follows;
ΔP = F/A
ΔP = mg/πr²
ΔP = (23 x 9.8)/(π x0.1²)
ΔP = 7,174.7 Pa
The gauge pressure inside the cylinder is calculated as follows;
Pi = ΔP + Po
Pi = 7,174.7 + 101325
Pi = 108,500 Pa
The height of the piston is calculated as follows;
[tex]\frac{V_1}{T_1} = \frac{V_2}{T_2} \\\\\frac{Ah_1}{T_1} = \frac{Ah_2}{T_2} \\\\h_2 = \frac{T_2h_1}{T_1} \\\\h_2 = \frac{(13 + 273) \times 0.86}{(307 + 273)} \\\\h_2 = 0.424 \ m[/tex]
h₂ = 42.4 cm
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