A Carnot engine operates between two reservoirs with efficiency 1/3. When the temperature of the cold reservoir is raised by x, its efficiency decreases to 1/6. If the hot-reservoir temperature is 99°C, x is:
Options

Question

A Carnot engine operates between two reservoirs with efficiency 1/3. When the temperature of the cold reservoir is raised by x, its efficiency decreases to 1/6. If the hot-reservoir temperature is 99°C, x is:

Options

G1 Physics · Accepted Answer

Tₕ = 99 + 273 = 372 K η = 1 - T꜀/Tₕ Initially: 1/3 = 1 - T꜀/372 T꜀/372 = 2/3 T꜀ = 248 K After raising the cold-reservoir temperature by x: 1/6 = 1 - (248 + x)/372 (248 + x)/372 = 5/6 248 + x = 310 x = 62 K Hence option D.