Question 999: Thermodynamics & KTG

Question

0.5 mole of an ideal gas at constant temperature $$27^{\circ} \mathrm{C}$$ kept inside a cylinder of length $$L$$ and cross-section $$A$$ closed by a massless piston. The cylinder is attached with a conducting rod of length L$$_1$$ cross-section area $$(1 / 9) \mathrm{m}^2$$ and thermal conductivity $$k_1$$ whose other end is maintained at $$0^{\circ} \mathrm{C}$$. If piston is moved such that rate of heat flow through the conduction rod is constant then velocity of piston when it is at height $$L / 2$$ from the bottom of cylinder is (neglect any kind of heat loss from system)

Accepted Answer

$$\frac{\Delta Q}{\Delta t}=\frac{\Delta W}{\Delta t}=$$ work done per unit time
$$\frac{d W}{d t}=P \frac{d v}{d t}=\frac{k a Q}{L}$$
as $$P=\frac{n R T}{v} \Rightarrow v=\frac{k a}{R}\left(\frac{27}{300}\right)=\frac{k}{100 R}$$

Answer

$$(\mathrm{k} / R) \mathrm{m} / \mathrm{s}$$

Answer

$$(\mathrm{k} / 10 R) \mathrm{m} / \mathrm{s}$$

Answer

$$(\mathrm{k} / 100 R) \mathrm{m} / \mathrm{s}$$

Answer

$$(\mathrm{k} / 1000 R) \mathrm{m} / \mathrm{s}$$

Thermodynamics & KTG

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