Suppose an ideal gas follows the process VP^3 | vedclass

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(B) Given the process equation: $VP^3 = k$ (where $k$ is a constant).From the ideal gas law, $PV = \mu RT$, we can write $P = \frac{\mu RT}{V}$.Substi

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$9T$

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(B) Given the process equation: $VP^3 = k$ (where $k$ is a constant).From the ideal gas law, $PV = \mu RT$, we can write $P = \frac{\mu RT}{V}$.Substituting $P$ into the process equation: $V \left( \frac{\mu RT}{V} ight)^3 = k$.This simplifies to $V \cdot \frac{(\mu R)^3 T^3}{V^3} = k$, which gives $\frac{T^3}{V^2} = 	ext{constant}$.Therefore, $\frac{T_1^3}{V_1^2} = \frac{T_2^3}{V_2^2}$.Given $T_1 = T$, $V_1 = V$, and $V_2 = 27V$, we substitute these values:$\frac{T^3}{V^2} = \frac{T_2^3}{(27V)^2}$.$\frac{T^3}{V^2} = \frac{T_2^3}{729V^2}$.$T_2^3 = 729T^3$.Taking the cube root of both sides, $T_2 = \sqrt[3]{729} T = 9T$.

Suppose an ideal gas follows the process $VP^3 = \text{constant}$. The initial temperature and volume of the gas are $T$ and $V$ respectively. If the gas expands to $27V$, then its final temperature will be:

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