Question

0.5 mole of an ideal gas at a constant temperature of 27°C is kept inside a cylinder of length L and cross-section area A, closed by a massless piston. The cylinder is attached to a conducting rod of length L, cross-section area A/19, and thermal conductivity k, whose other end is maintained at 0°C. The piston is moved such that the rate of heat flow through the rod is constant. The constant velocity of the piston when it is at height L/2 from the bottom is 

• A. \( \dfrac{k}{R}\,\text{m/s} \)
• B. \( \dfrac{k}{10R}\,\text{m/s} \)
• C. \( \dfrac{k}{100R}\,\text{m/s} \)
• D. (k)/(1000R)m/s

Hint:

Isothermal processes require continuous heat exchange to maintain temperature.

Answer 1

The Correct Option is B

Step 1: Rate of heat flow through rod: Q = (k(A/19)(27))/(L)
Step 2: For isothermal process: Q = P(dV)/(dt)
Step 3: Using ideal gas law P = (nRT)/(V) and V = A(L)/(2), Q = (nRT)/(V)A v
Step 4: Substituting values and solving, v = (k)/(10R)