Question

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We Often have the experience of pumping air into bicycle tyre using hand pump. Consider the air inside the pump as a thermodynamic system having volume V at atmospheric pressure and room temperature,27°C. Assume that the nozzle of the tyre is blocked and you push the pump to a volume 1/4 of V. Calculate the final temperature of air in the pump? (For air, since the nozzle is blocked air will not flow into tyre and it can be treated as an adiabatic compression).Take γ for air = 1.4.​

Answer 1

Answer:-

$\red{\bigstar}$ The final temperature of air in the pump is $\large\leadsto\boxed{\rm\purple{522 \: K \: or \: 249^{\circ} C}}$

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• Solution:-

Here, the process is adiabatic compression.Therefore, the equation

$\pink{\bigstar}$ $\large\underline{\boxed{\bf\green{T_i V_i ^{\gamma -1}}}}$

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➪ $\sf T_i = 300K(273 + 27^{\circ} C = 300 K)$

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➪ $\sf T_i V_i^{\gamma -1} = T_f V_f^{\gamma -1}$

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➪ $\sf V_i = V \& V_f = \dfrac{V}{4}$

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$\pink{\bigstar}$ $\large\underline{\boxed{\bf\green{T_f = T_i \bigg(\dfrac{V_i}{V_f}\bigg)^{\gamma -1}}}}$

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➪ $\sf T_f = 300 \: K \times 4^{(1.4-1)}$

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➪ $\sf T_f = 300 \: K \times 4^{(0.4)}$

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➪ $\sf T_f = 300 \: K \times 1.741$

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➪ $\sf T_f = 522.3 \: K$

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★ $\large{\underline{\underline{\bf{\red{T_f \approx 522 \: K}}}}}$

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✯ Therefore, the final temperature of air in the pump is 522 K or 249° C.

Answer 2

Answer:

Given :-

• Consider the air inside the pump as a thermodynamic system having volume V at atmospheric pressure and room temperature , 27 degree celcius.Assume that the nozzle of the tyre is blocked and push the pump to volume 1/4 of V.

□To find :-

• Final temperature of air in pump.

□Solution :-

• In the hint given that,
• adiabatic compression therefore the equation is
• $TiV {i}^{ \gamma - 1}$
• Therefore, By applying the values we get that, we get equation as,
• $Ti = 300k(273 + 2 {7}^{0} c)$
• $TiV {i}^{ \gamma - 1} = TfV{f}^{ \gamma - 1}$
• $Vi = \frac{V}{4}$
• Therefore,
• $Tf = Ti( \frac{Vi}{Vf} ) {}^{ \gamma - 1}$

♧Now, by applying values we get that,

• $Tf= 300K \times {4}^{(1.4 - 1)}$
• $Tf = 300K \times 1.741$
• $Tf = 522.3K$

□Hence ,

• The final temperature of air in pump is 522.3K.

♧Hope it helps u mate .

♧Thank you .