Question

A containers volume is reduced by 75% And the gas inside had an initial temperature of 10 degrees Celsius. What is the final temperature in degrees Celsius if it compressed polytropically with n= 1.45

Answer 1

Answer on Question #45008 – Physics – Molecular Physics | Thermodynamics

Question.

A containers volume is reduced by 75% And the gas inside had an initial temperature of 10 degrees Celsius. What is the final temperature in degrees Celsius if it compressed polytropically with n= 1.45

$$V_2 = 0.25V_1$$ $$T_1 = 10{}^\circ\mathrm{C} = 283\ \mathrm{K}$$ $$n = 1.45$$ $$T_2 = ?$$

Solution.

The polytropic equation:

$$PV^n = const$$

But from the equation of ideal gas we know

$$PV = RT \rightarrow \frac{PV}{T} = R = const \rightarrow P = \frac{const}{V} T$$

Therefore,

$$TV^{n-1} = const$$

In our case,

$$T_1 V_1^{n-1} = T_2 V_2^{n-1} = const \rightarrow T_2 = T_1 \left(\frac{V_1}{V_2}\right)^{n-1}$$

Calculate:

$$T_2 = 283 \cdot 4^{0.45} = 283 \cdot 1.866 = 528.1\ \mathrm{K} = 255.1{}^\circ\mathrm{C}$$

Answer.

$$T_2 = T_1 \left(\frac{V_1}{V_2}\right)^{n-1} = 528.1\ \mathrm{K} = 255.1{}^\circ\mathrm{C}$$

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